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 =

$\frac{1}{2}\cdot b_1\cdot h$

The area of the triangle B =

$\frac{1}{2}\cdot b_2\cdot h$

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

$\frac{1}{2}b_1\cdot h+\frac{1}{2}b_2\cdot h_{}$

Take 1/2 h as a common:

$=\frac{1}{2}h\cdot(b_1+b_2)=\frac{1}{2}\cdot h\cdot b$

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