How to find the area of a triangle in a square?

Knowing about areas of different shapes is very important from a mathematics point of view. Also, knowing of areas of shapes embedded between another shape is also very important to know. They have many interesting properties which we will be studying on this page.

Answer: The area of a triangle in a square is equal to half the area of the square.

Let's understand in detail.

Explanation:

Let's consider the figure given below, having a triangle embedded inside a square.

The length of the square ABCD given is 10 units.

Hence, the area of the square ABCD is 100 sq. units.

Now, if we draw a line parallel to AD and BC passing through point O, then we will notice that the first half of the triangle DOC will be congruent to AOD, and the second half will be congruent to OBC.

As congruent triangles have the same area, we will get 2 (area of OBC + area of AOD) = 100.

Hence, we get the area of the triangle shaded as 50 sq. units.

Hence, the area of a triangle in a square is equal to half the area of the square.