The geometry math problem that makes you think twice

追加: 2026-05-31

[00:00:01]We are asked to find the area of the shaded portion. Welcome back to my channel. First of all, let us draw out the parts that we can see here. Okay.

[00:00:11]Different types of um shapes that we can see.

[00:00:18]First, let's join A to D.

[00:00:22]Let's join A to D.

[00:00:32]Okay. Now having done that um this question people fail it a lot but I don't know why students are failing it because it's actually very easy. So if you look at this now we have three shapes that we can see. The first one is we can see a quadrant. This you can see a quadrant and the quadrant is a c d a c d because this is 90°. So this is a quadrant right? So if we have that this part of the what this part that's what I'm representing now we have another part that we can see if you look at this we can from here we can draw out what this particular triangle so let's draw triangle A C D A C D. Okay. So let's find the area of this quadrant and also find the area of this triangle. Then you're going to see how we are going to use this to actually find the area of the shaded portion.

[00:01:47]If this is the first time you are seeing this lovely channel, please hit the subscription button. Turn your notification bell. Yes. So that you don't miss our videos. We always upload our videos as often as possible to at your convenience. There must be something new for you to watch. All right. Give us a thumbs up if you love what we are doing. All right. Now, looking at this drawing, like I said, we're going to find the area of the triangle and that of the quadrant. First thing we have a C. This is a square.

[00:02:23]Okay, I forgot to mention that that this is a square. And if this is a square that means if this is two this is two this side is two and this side is two as well. So a c is equal to b c which is equal to c d is equal to a d. So a c is 2 c d is 2 as well. Now let's find area.

[00:02:50]Area of a triangle is half base. Right?

[00:02:55]So the area is equal to the base * the height / 2.

[00:03:02]The base time the height / 2. The base is two. The height is two.

[00:03:10]So we have 2 * 2 / 2. So this we remove this. We have two. So this is 2 units squared.

[00:03:23]The area of the triangle is 2 units squared.

[00:03:29]So if you look at this now we have a quarter circle or a quadrant. Now area of a circle is p<unk> r² right area of a circle is p<unk> r².

[00:03:48]Now area of quarter circle will be pi r² divided by 4.

[00:03:56]So as usual a c is 2 c d is 2 as well. Okay.

[00:04:06]Now the radius of this circle is 2.

[00:04:12]So the area of the quadrant will be<unk> * 2^ 2 / 4<unk> r² / 4. So we're going to have<unk> * 4 / 4.

[00:04:33]This we remove this and we have pi. So the area of the quadrant is pi.

[00:04:40]The area of the triangle is two 2 units squared. So this is pi unit squared.

[00:04:48]Then we are asked to find the area of the shaded portion. How are we going to make use of this and this to find the area of the shaded portion is actually something you can do easily. Okay. You can see that this is part of this. So if we should take away the area of this triangle from the area of this quarter circle, we are going to find the area of this part. This one on top, right? We're going to find it. So let's go ahead and do that. Area of the quarter circle minus area of the triangle will give us this area. This one I'm shading now. All right.

[00:05:31]Now area of the quadrant is pi and area of the triangle is 2. So let's go ahead and do that.

[00:05:42]So area of the shaded portion because this is half of it will be equal to area of the quadrant minus area of the triangle. Okay. So it's going to be area of the quadrant give us pi minus area of the triangle give us 2. So this will be unit squared right.

[00:06:08]But we are actually looking for the total area of the shaded portion. So if half of the shaded portion the area of half of the shaded portion is minus 2 that means that the area of the whole shaded portion will be equal to. So area of the shaded portion now will be equal to 2 *<unk> - 2 unit 2. So if you open the bracket you have 2 *<unk> is 2 pi 2 * 2 is 4. Now pi is 3.14 right? Now 3.14 * 2 will give you 6.28. 28 - 4.

[00:06:57]If we solve that, we will have sorry - 4. It's supposed to be like this. So, we're going to have approximately 2.28 units squared as the area of this particular shaded portion. Thank you so much for watching and see you in my next video. Bye.