Question

4. The triangle shown is composed of two triangles where b, + b = b. Verify that the area of the entire triangle is equivalent to the sum of the areas of Triangles A and B.

Answer 1

Given : the triangle shown is composed of two triangles where

`b_1+b_2=b`

The height of both triangles is the same as the height of largest triangle

The area of the triangle A =

`(1)/(2)\cdot b_1\cdot h`

The area of the triangle B =

`(1)/(2)\cdot b_2\cdot h`

The sum of the area of the triangles A and B =

`(1)/(2)b_1\cdot h+(1)/(2)b_2\cdot h_{}`

Take 1/2 h as a common:

`=(1)/(2)h\cdot(b_1+b_2)=(1)/(2)\cdot h\cdot b`

So, the area of the entire triangle is equivalent to the sum of the areas of Triangles A and B. ​