Question

find area of quadrilateral BCED​

Answer 1

$\large{\blue{\implies{Given}}}$

In ∆ABC , Ratio of the sides : AD/DB=AE/EC=2

area of ∆ABC=36cm^2

$\large{\blue{\implies{To\:find}}}$

Area of quadrilateral (BCED)

$\huge{\mathcal{\blue{\underline{Answer}}}}$

✨ AD/BD=AE/EC=2

[ Hence the line joining the two sides of the triangle divides the sides of the triangle in the same ratio ]

✨Therefore , the ∆ADE~∆ABC

first ,we have to find the area of ∆ADE

Applying theorem :

The ratio of the areas of two similar triangle is equal to the square of the ratio of thier corresponding sides

∆ADE/∆ABC=(AD/DB)^2

∆ADE/36cm^2=1/4

∆ADE=9cm^2

Area of quadrilateral (BCED)= Area of (∆ABC-∆ADE)

=36cm^2-9cm^2

$= 27cm {}^{2}$