Parallelogram - Measurements || SSC CGL 2026 {Part-2}

Added: 2026-05-05

[00:00:01]First of all, thanks for being here in my YouTube channel. So friends, in this video we are going to learn one of the important concept on a measurement topic that is parallelogram for this year SSC CGL exam. Right? So first let's take parallelogram. If if you are preparing for the SSE exam or any competitive exam, mostly students won't give that much importance to the topic parallelogram because they think if I learn rectangle, parallelogram is easy.

[00:00:30]Yes, if you learn a rectangle, most of the concept what we learn on a rectangle which is equals to parallelogram. But remember that if it is a square, if it is a rectangle or a circle for all these kinds of questions in your exams you can able to see the questions that they will be asking us to find find the area of a circle find the costing for the floor.

[00:00:54]So these kinds of questions you can able to see on circle square and rectangle.

[00:01:00]If you take parallelogram, trapezium, uh, rhombus, quadrilateral for all these two-dimensional shapes, most of the question will be like find the value of x, not the area, not the diagonal, not the perimeter. Our target is to find what is the value of x. So if you need to solve the value of x, you need to know the property of it. So remember that if you are preparing for the any competitive exams for a parallelogram not only parallelogram parallelogram rhombus quadilateral trapezium for all these first learn the properties properties will be the important role for all these dimensional shapes. So first learn the property try to understand that how this property and what is the different from all these shapes. How the property makes the shapes different. So you have to learn all these stuff and solve the question which is related to property and then you can able to solve area perimeter those kinds of question will be very easy but understanding the property and applying the property on the question is most important for the competitive exams right. So friends now in this video we will be learning the first let let's learn the properties of a parallelogram.

[00:02:14]What are all the important properties are there and one important diagonal formula. So once you learn the diagonal formula you can able to solve the maximum number of question and understand that while solving a parallelogram question at some point you can able to see a triangle formula will be applied here. See we are learning a parallelogram but in the parallelogram what in in some question they will be using a triangle formula. So you have to understand that why the triangle formula has been used in the parallelogram.

[00:02:44]Usually in a parallelogram we have a sides but the area of a parallelogram will be base into it where the it comes in. So you have to learn all these stuff before solving a question. So once you understand the parallelogram concept and the property solving any question will be very easy. Right? So first let's learn what is actually how the parallelogram looks like. So parallelogram is nothing like we know how the rectangle will be. So if you have a small tilt like this which is which act as a parallelogram. So two parallel lines right. So let let's take this as one set of parallel line and this will be another set of parallel line. So now this is called as a parallelogram. Right? So yes. So friends remember that if if it is a parallelogram the major property of the parallelogram is opposite side length will always be equal. For example, if this length is 13 cm, so the opposite side will also be 13 cm. If this is 4 cm, then the opposite side of the parallelogram will also be 4 cm. So the first property is opposite sides of a parallelogram the length will always be equal. So that will be the first property and second thing is it's not a property. Now the second thing what we are going to learn here. So first we have to understand the question values like rectangle if it for for example the length and breadth of the rectangle has been 13 cm and 4 cm. So we have to understand that which value is length and which value is breadth. So there are two different way they can denote this 13 cm and 4 cm in a parallelogram. So the first way is the sides of the parallelograms are so the sides of a parallelogram are 13 cm and 4 cm. See they didn't mention that which side is 13 cm and which side is 4 cm. They just mentioned that the sides of a parallelogram are 13 cm and 4 cm. So always understand like the what we learned in the rectangle the larger side larger number 13 number this should always be taken as the base in a rectangle we call it as a length and we call this number as a breadth in a parallelogram we call this value as a base value. So base of a parallelogram and this is a side of a parallelogram not the sides one side one side of the parallelogram and this will be the base always if they have given the sides of the parallelograms as two numbers so consider the larger number always as a base in some questions you can able to see the base of a parallelogram is 14 cm and side is 3 cm. So now this will be easy right? So they have given the direct value where the base is 14 cm and the side is 3 cm. So some students will ask them can I take this as a side? Yes, all the four things are assumed as a sides of a parallelogram. But remember that while drawing a perfect parallelogram, we always consider the base value as the larger value. So here this should be considered as 14 cm and this should be considered as 3 cm. It's not the property just we need to understand the question values right. So first thing we have learned opposite sides are always equal and now we have learned how to find out from the given question value how we need to assumed it in the diagram right. So always the larger value should be considered as a base. So now coming to the point in a measurement of in the while solving a measurement question in a parallelogram.

[00:06:31]So three major thing that we can able to find from this dimension. One is the area of a parallelogram and second is the diagonal of a parallelogram. Any one diagonal and the third important is perimeter of a parallelogram. Right? So now perimeter.

[00:06:48]So perimeter is what? Nothing but adding all the four sides length which is called as a perimeter. So we already know that the rectangle rectangle perimeter of a rectangle is what? Two times length and breadth. So here also we have two times same length and two times same this breadth. But it's called as a side. So here also we can say two *s of a plus b. They they didn't call it as length and breadth. They call one side as a another side as b. So perimeter of a parallelogram and perimeter of a rectangle both are same.

[00:07:18]So two times of a + b. So now now coming to the two important concept. One is area. Area of a parallelogram. Right? So what is the formula for area of a rectangle? Area of a rectangle is length into breadth. But when it comes to a parallelogram area of a parallelogram will be base into not the side base into height. So where this it comes from in the diagram we have only base and the side then where this it comes in the parallelogram where this I value comes in comes from the parallelogram right.

[00:07:53]So I will draw one diagram and show you.

[00:07:55]So try to assume that right? So understand how I'm drawing the diagram.

[00:07:59]How we are multiplying? That's the reason we are multiplying. Area is equals to base into height. So all these things will you can understand from the diagram what I'm going to draw. Now just listen carefully. We know that how the parallelogram looks like. So this is the parallelogram right? So now what I'm going to do is just drawing this will not exactly 90°. This will be like small small tilt will be there somewhere around some angle less than 90°. So if I draw a straight line here from this point, this is called as a it is called as the height of the parallelogram. So why we are in order to find the area of a parallelogram the reason for multiplying the base and it is just listen carefully just listen just assume this what I'm going to do if I'm cutting this part alone right if I cut this part this is the part right in this parallelogram if I cut this part and join the same now you can see this is the straight line right so this act as a straight line here which is the height so this cut area alone. If I joined in here in the last part of the parallelogram, see if I join the same thing here. So you can see yes. So now this will be height and this is what the complete base. So now when you look at the diagram carefully, so if you erase this part now you can see the parallelogram has become a rectangle.

[00:09:33]Yes or no? Now initially first time I drawing it's a parallelogram that part alone I just cut it and joined with the last at the end. So now you can able to see the base into it. Now the complete diagram turned into a rectangle. So that's the reason for finding the area of a parallelogram they multiply the base into height. So area of the parallelogram will be base into not the another side base into height. So friends understood or not? So in order to find the area of a parallelogram you have to mean that base will always be same but height where it comes from where the that height comes. So you you should know this part in your mind. So that's the reason we are multiplying in order to find the area of a parallelogram base into height. Right?

[00:10:20]So first thing and then you have to understand another one important concept here in the parallelogram is in some cases not in all the cases in some cases while solving a question the reason for applying a triangle formula because it's a parallelogram right there is no relation between triangle and a parallelogram. Why they are applying a triangle formula in some cases in the parallelogram just just see here if let's take this as a one parallelogram right if you draw a diagonal value diagonal if if I draw a diagonal like this yes so now this diagonal line what it makes it it makes the parallelogram into two triangle yes or no because if I draw a diagonal line so this will be one triangle and this will be another triangle. So by drawing a diagonal in a parallelogram which makes the parallelogram into two triangles. What is the area of a triangle formula of BH? So one triangle area which is half into B into H. So now because of drawing a diagonal line in a parallelogram this makes two equal triangle that means the area of both the triangles are equal. So here we know that area of one triangle will be half big h. In order to find area of two triangle which will be 2 into half big h. So we can cancel two and two here resultant will be b and h which will be the area of complete parallelogram. Yes or no? area of a parallelogram formula is base into height. So how the base into height comes is because of two triangles which merge resultant will be the parallelogram and both the triangle area will be same. So that's the reason area of one triangle is half big. There are two triangles in a parallelogram. So 2 into half big we can cancel two and two resultant will be base and height.

[00:12:21]So that's the formula for area. So friends understood. So we have to learn deeply only then we can able to solve some tire two question that's the reason I'm teaching all these stuff and yes now you hope you understood the perimeter formula and you know the area formula last is the diagonal so coming to the point of diagonal right so here you have to understand that there are two diagonals in a parallelogram so this will be one diagonal and this will be another diagonal so let let's assume this as diagonal one and this is diagonal two always Remember that both the diagonal length will be different.

[00:12:58]So friends understood both the diagonal length. So let's take diagonal one and diagonal two. So friends listen carefully here in in the two diagonals where we already know that both the diagonal length are not equal. But if you take the one diagonal alone this part this length and this length will be equal. So friends understood or not these two full diagonal length are different. But when you take diagonal one alone right so this length will always be equals to the same another part of the diagonal length. So if this is 13 cm then this will be 13 cm. If this diagonal to 4 cm and this will be 4 cm. So friends understood always the diagonal which cut bisects right. So these two diagonal length will be different but when you take one diagonal the two part will be equal. So that's the important property in this parallelogram. Right? And we have a diagonal formula. I will write the diagonal formula. D1 squared diagonal 1 square + diagonal 2² is equals to 2 * of a² + b square. It's one of the important formula in the parallelogram because in most of the question they will give you diagonal values and one side will not be given. In some question they will give you both the side and one diagonal and one diagonal value will not be given.

[00:14:18]Remember that in the books you will find multiple formulas but all the formulas in the parallelogram is derived only from this. So better you can learn this formula alone for finding one diagonal value it will be like cos theta sin theta formula. I hope uh that much level questions will not be asked in your exam. So it is better to learn this diagonal formula alone which is important for the parallelogram. Right.

[00:14:44]So next thing is you have to know other than this we have learned the diagonal formula and we have learned the area formula and then we have learned the perimeter formula. So other than this you have to know some important properties of a parallelogram that is based on a geometry also. Right? See if you take a parallelogram remember that the opposite angles will always be equal. For example let's take in a parallelogram we have four angles right?

[00:15:12]So 1 2 3 and four. So here what they are saying is the opposite angles are equal.

[00:15:19]For example, if this is 45° then this angle will also be 45°. So the opposite angles will be equal. So that is the one property of a parallelogram. And another important property is when you add the adjacent angles nearby angles. For example, if this angle is 45°, what is the adjacent angle of this? Either this or this nearby angles. So when you add the adjacent angles, which should be equals to 180°, the sum the sum of two angles should be equals to 180°. If you add these two angles, resultant will be 180°. If you add these two angles, resultant should be 180°. Again, these two top two angles 180°. So when you add all the any two adjacent angles that should be equals to 180° and the opposite angles will be equal right. So friends I think this is enough you don't want to uh learn in depth about parallelogram this is okay to solve all the questions on SSE and railway for the upcoming exams. So remember that we have learned the most most important concept.

[00:16:31]Don't think that the parallelogram is the easy part. Many questions you can see from the exams that will be asked on the parallelogram sessions. So for solving a parallelogram session you have to know all these properties. Let me have a quick recall about the parallelogram. So first you know how the parallelogram looks like and second is the sides of a parallelogram or base and side. You have to understand that the always the larger value it's assumed as a base. And now in the parallelogram we have three major things to find. One is the area of a parallelogram and second is the perimeter of the parallelogram and third is the diagonal. First let's talk about the perimeter of a parallelogram. So perimeter of the parallelogram and perimeter of the rectangle both are equal. So the same formula 2 * of a + b. So now coming to the area of the parallelogram. So area of the parallelogram will be equal to base into height. So I have just now I have told you in the diagram where this height comes from and how why we are multiplying base into height resultant will be area and how we make the parallelogram into rectangle. So all these stuff I have taugh in this video.

[00:17:33]I hope you understood that understood that concept right? That's the reason we are multiplying base into it. And the third important thing is the diagonal.

[00:17:41]Before a diagonal thing I have just mentioned one one important concept that is if you draw a diagonal line in a parallelogram it splits the parallelogram into two equal half that means two equal triangle area. So one triangle area will be half big. So once you multiply into two 2 into half b we can cancel 2 and 2 which is base into height. That's the reason we got the area of the parallelogram formula is equals to base into height. While solving some tough level questions you can be able to find they will apply the triangle formula here. That is the reason right. So friends and the last is the diagonal. So this is one of the important formula. Learn this formula in a parallelogram because most of the question they will give you two diagonal length and we have to find one side of the parallelogram. So by using this formula we we can easily find any values that is based on the parallelogram right and then at last it's it's an important concept in a parallelogram that is based on an angle always the opposite angles of a parallelogram will be equal and when you add the adjacent angles of a parallelogram which is equals to sum which is equals to 180° right so friends now let me move on to some of the question which is related to the property and that was asked in the previous year from 2022 on various competitive exams so that you will get an idea right how to solve a question that is based on property and based on a formula. So here is the first question.

[00:19:09]So when this was the question that was asked in air force exam 2023 right. So just see they have given a diagram and they mentioned two values. So 3x + 5 and 5x - 7 in the diagram and our target is to find what is the value of a d. So here when you look at this dimension you can we can easily say it's a parallelogram in the question also they mentioned in the given figure in the parallelogram they have mentioned that a is 3x + 5 e d 5x - 7 so they have given all the values so now in order to find the value of a d which is the diagonal always remember that you have to understand that whether this question should be solved by using the property what we learned or the formula If it is finding the value of x or based upon the angles always remember that we have to apply the property. What is the property we learned just now? We have learned one property. Always remember that the diagonal opposite diagonal length will be different. But when you take one diagonal which bisects another diagonal but in this area in this point where you can able to understand one concept this diagonal length and this diagonal length will be equal. That means the length of Ae. So Ae will always be equals to E d. So now we can equate both the values equation. So 3x + 5 is equals to 5x - 7. So once you bring this 3x towards right hand side, it becomes 5x - 3x will be 2x. So when you bring this - 7 towards left hand side, this will be 12. So finally we got x is equ= to 6. That means we found the value of x= to 6. Substitute in any one side.

[00:20:55]So we already know that a is how much?

[00:20:58]3x + 5. So substitute x is equals to 6 here. So 6 into 3 will be 18. So 18 + 5.

[00:21:06]18 + 5 will be 23. So if this length is 23, then this will also be equals to 23.

[00:21:15]So now we can say that find the value of a. So the total length of the diagonal one which will be 46. So that's is the that is the answer for this question. So friends understood or not always remember that to find the value of x not only in parallelogram the same questions can also be asked in trapezium rhombus quadrilateral. So remember every everywhere the property changes but remember that this kind of question you should solve only by applying the property. Right? So friends answer for the first question is the value of a which is equals to 46 cm. So friends here is the second question. So here our target is to find in this parallelogram question our target to find the value of x. So how will you find it? Just now just see the question to find the value of x we we should not use the formulas perimeter area diagonal formula. We have to apply the property. What is the property here? Just now we have learned one important property that is based on an angle of a parallelogram. So always the opposite angles will be equal or else when you add the adjacent angle which is equals to 180°. Here you can able to see in the parallelogram diagram they have given the opposite angles. So we know that the opposite angles will always be equal in a parallelogram just equated. So 6x - 15 is equals to 3x + 30. That's it. So if you bring this 3x towards left hand side 6x - 3x will be 3x. So this will be 45 because -5 + 30 will be 45. So x is equals to 15. That's it. So we can say that the value of x is equals to 15. If you want to find one angle just substitute 15 here you will get one angle. So if you got one angle that will be resultant to the opposite angles. Right? So now I hope you understood how to solve a question that is on a parallelogram that is related to a property. So same thing with they can ask you in a different different way.

[00:23:10]For example the same 6x - 5 they can ask you like the 6x - 15 3x + 30. So our target is to find what is the value of x. How will you find? We already know that if it's a parallelogram opposite sides are equal equate both or else they ask us to find find the value of x + y.

[00:23:28]So they will give you an equation like this 4x + 3 3 y + 9. So find x + y.

[00:23:39]So they will give you a parallelogram and they will give you all the sides in terms of equation. Our target is to find what is the value of x and y. How will you solve? We have to equate these two.

[00:23:50]Find the value of x. Equate these two.

[00:23:53]Find the value of y and then add the two value.

[00:23:57]Resultant will be the sum of x and y. So when understood? So the property plays a major role. So to solve this question, let me solve another one question which is related to the formula. So friends, here is the last question of this video.

[00:24:12]So the length of diagonal of a parallelogram are 10 <unk>3 and 10 <unk>2 cm. If one side of the parallelogram is 13 cm, find the perimeter of it. Right? So here this question our target is to find the perimeter. So if we need to find the perimeter or if we need to find the area or a diagonal. So for all these we have to apply the formula not the property.

[00:24:36]So in previous two question we have not applied the formula because the question is based on a property side. So read the question carefully understand that whether the question has to be solved by using a formula or by a property and then you can proceed by the way that whether formula or a property method.

[00:24:53]Right? So here our target is to find what is the perimeter of the parallelogram. What is the formula for perimeter? So perimeter of a parallelogram which will be equal to perimeter of a rectangle. So 2 *s of a + b. So one side and another side. So this is the formula that we have to use to find the perimeter of a parallelogram.

[00:25:11]And according to the question so they have given let let me draw the diagram here. Right? Assume that uh they have given one diagonal two diagonal length has been given. One diagonal is 10 <unk>3. Let's assume this as 10 <unk>3 and another diagonal of a parallelogram which is 10 <unk>2 and one side has been given that is 13 cm. So by using this value our target is to find what is the perimeter of the parallelogram. So perimeter is nothing but adding all the four sides. We have one side which is 13 cm but another side is unknown. So by using a formula just now I have told you what is the diagonal form not the diagonal formula if they have given a diagonal and one side has been given or else they have given the sides of a parallelogram and the diagonal was not given we can use that one formula that is enough where you can find most of the values in the parallelogram right so here our target is to first initially find other side of the parallelogram and then we can find the perimeter of it right so first just now we have learned the formula diagonal 1 square plus diagonal 2 square is equals to 2 * of a square + b square right. So a square will be one side b will be another side and this will be diagonal 1 and diagonal 2. So according to the question they have given the diagonal 1 value which is 10 <unk>3 the whole square plus 10 <unk>2 the whole square let me multiply two inside which will be 2 a² and 2 b² so a square let's assume that as a first side which is 13 cm. So 13 squar + 2 b².

[00:26:45]So this value is unknown. Another side is unknown. So let me keep the b as it is. So 10 squar is 100 <unk>3 squar is 3. 100 into 3 will be 300. So similarly plus 10² is 100 <unk>2 square is 2 100 into 2 will be 200 is equals to 2 into 169 + 2 b². So now this will be 500. So minus of 9 2's are 18 remaining will be 1 1213 remaining will be 1. So 2 and 3.

[00:27:18]So 338 is equals to 2 b². So 338 500 - 338 will be 162.

[00:27:27]So 162 is equ= to 2 b². Let's cancel this will be 81. So b ² is equal to 81.

[00:27:35]So b will be 9. So B is nothing but another side of the parallelogram because one side of the parallelogram has been given which is 13 cm. So now we got the another side which is 9 cm. So according to the question they have given they have not given one side of the parallelogram. So by using that diagonal formula what we learned initially we have applied all the values in the formula and we got another one side right. So now we have to find the perimeter according to the question our target is to find the perimeter. So now it is easy right? So perimeter is equals to 2 * of 13 + 9 will be 22. So 22 into 2 will be 44. So all the values are in cm. So perimeter will be 44 cm. So which will be the answer for this question.

[00:28:18]Right? So friends in this video we have learned lot more things like parallelogram important properties and how to find whether the question has to be solved by using a property or by a formula that is important. So parallelogram, trapezium, quadrilateral, rhombus. So for all these measurements, dimension, two-dimensional shapes. First learn the property not the formula.

[00:28:43]Learn the property. Understand that how these shapes are differ from everything.

[00:28:48]So learn the property and try to solve the question. How to find the value of x by using the property and then solve a question like area, diagonal, those things are easy, right? So only thing is learning the property will help you to solve most of the question on these four dimensional images right. So friends thank you so much for watching this video. So whenever you get time uh try to write the test series what I have given I have given the all the topics list of topics as a test for SSC as well as railway this year. So don't forget to purchase it and start writing the test.

[00:29:22]And uh if you have more free time just watch all my YouTube videos where I have posted on aptitude reasoning everything is there in the playlist. So have a proper schedule proper preparation will definitely help you to clear the exam this year. So friends, thank you so much for watching this video and bye.