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In the given figure, ABCE is a parallelogram. P is the midpoint of AD and AD ⊥ EC. If AD=20 cm and EC=18 cm, find the area of the given figure.

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300 {cm}^{2}

280 {cm}^{2}

270 {cm}^{2}

290 {cm}^{2}

answer is C.

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Detailed Solution

Given,
ABCE is a parallelogram, AD||DC and AD⊥EC.
AD’s mid-point is P,
Also,
EC=18 cm
AD = 20 cm
We know that,

AP = PD

(PD= AD/2)

AP = \frac{20}{2}

AP = 10 cm

Parallelogram ABCE area,
A= EC×AP

A = 18 \times 10

A = 180 {cm}^{2}

Now, triangle ECD area can be given as,

= \frac{1}{2} \times EC \times PD

= \frac{1}{2} \times 18 \times 10

= 90 {cm}^{2}

Now,
Area= ABCE parallelogram area+ ECD triangle area

Area = 180 + 90

Area = 270 {cm}^{2}

Thus, the value of area is

270 {cm}^{2}

.
So, the correct option is 3.

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