What's the Area of This Triangle? Most Get It Wrong

Added: 2026-05-13

[00:00:00]Hello everyone.

[00:00:01]In this video, I am going to solve an interesting geometric problem.

[00:00:07]We have a triangle.

[00:00:10]Consider this triangle is A B C The side length of AB is 12 unit and the length of AC is equal to 18 unit.

[00:00:30]And there is a point to this base. Consider this point is D such that BD is equal to DC is equal to AD.

[00:00:45]We have to find the area of this triangle ABC.

[00:00:55]As BD is equal to DC is equal to DA, so we can draw a circle through point B A and C whose center will lies on point D.

[00:01:17]Consider this circle is In this circle it passes through point B A and C and the center of this circle is D.

[00:01:32]Because this BD indicate the radius of this circle, this DC is also radius and DA, this is also the radius of this circle.

[00:01:43]So, BC is the diameter of this circle.

[00:01:49]So BAC, this angle lies on semicircle, so this angle is a right angle.

[00:02:04]That means this angle is 90°.

[00:02:10]So, this ABC is a right angle triangle.

[00:02:17]So, the area of triangle ABC is equal to half times base of this triangle. Consider this AB as base.

[00:02:34]So, AB times height of this triangle is AC.

[00:02:44]So, this is the area of triangle ABC.

[00:02:47]Now, substitute the value of AB and AC, we'll get half times AB.

[00:02:56]This is 12 unit, so 12 times AC. This is 18 unit.

[00:03:09]is equal to this two and this 18 divided by two is nine.

[00:03:19]And nine times 12 is 100 and eight.

[00:03:27]And this is the area of this triangle ABC.

[00:03:34]And this is the solution of our given problem.

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[00:03:46]Thanks for watching.