Question

in the given figure if AD/DB is equal to AE/EC is equal to 2 and area of triangle ABC is equal to 36 CM square find the area of quadrilateral BCED​

Answer 1

Area of the quadrilateral BCDE is 20 cm².

Step-by-step explanation:

From the given figure,

$\frac{AD}{DB}=\frac{AE}{EC}=2$

$\frac{AD}{AB-AD}=\frac{AE}{AC-AE}=2$

$\frac{AB-AD}{AD}=\frac{AC-AE}{AE}=\frac{1}{2}$

$\frac{AB}{AD}-1=\frac{AC}{AE}-1=\frac{1}{2}$

$\frac{AB}{AD}=\frac{AC}{AE}=1+\frac{1}{2}=\frac{3}{2}$

Therefore, ratio of areas of triangles ABC and ADE will be

$\frac{\triangle ABC}{\triangle ADE}=(\frac{3}{2})^{2}=\frac{9}{4}$

If area of ΔABC =36 cm²,

$\frac{36}{\triangle ADE}=\frac{9}{4}$

Then area of ΔADE = $\frac{36\times 4}{9}=16$ cm²

Now area of quadrilateral BCED = Area of ΔABC - Area of ΔADE

= 36 - 16

= 20 square cm

Therefore, area of quadrilateral BCDE is 20 cm².

Learn more about the similar triangles from

https://brainly.in/question/195212

Answer 2

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