Question

In a triangle ABC , DE parallel to BC. If DE = 2/3BC and area of triangle ABC=81cm2 , find the area of triangleADE ..?

Answer 1

de=2/3bc

de/bc=2/3

By ar.thm ar (ade)/ar(abc)=(de/bc)^2

ar(ade)/81=(2/3)^2

ar(ade)/81=4/9

Ar(ade)=36cm^2

Answer 2

Given: In a triangle ABC , DE parallel to BC. If DE = 2/3BC and area of triangle ABC=81cm2.

To find: The area of triangleADE.

Solution:

The angle A is common between both the triangles ABC and ADE. since DE is parallel to BC, the angle D is corresponding to angle B and hence, is equal to each other. Similarly, angle E is equal to angle C. So, the triangles ABC and ADE are similar to each other by the AAA (Angle-Angle-Angle) postulate.

Now, the following equation is given in the question.

$DE = \frac{2}{3} BC$

$\frac{DE}{BC} = \frac{2}{3}$

Thus, the ratio between the areas of the two triangles is equal to the corresponding side as follows.

$\frac{Ar. ADE}{Ar.ABC} = (\frac{DE}{BC} )^{2}$

$\frac{Ar. ADE}{81 cm^{2}} = (\frac{2}{3} )^{2}$

$Ar. ADE = \frac{4*81}{9}$

               $= 36 cm^{2}$

Therefore, the area of triangle ADE is 36 cm².