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In the following figure, $A B C D$ is a rectangle with sides $A B = 10 c m$ is a rectangle with sides and $A D = 5 c m$ and . Then the area of $Δ E F G$ . Then the area of from the options given below is:

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25 cm 2

35 cm 2

45 cm 2

55 cm 2

answer is A.

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Detailed Solution

Given that ABCD is a rectangle with sides AB = 10cm and AD = 5cm.
Question Image

We have to find the area of

Δ E F G .

Since ABCD is a rectangle,

D C | | A B

.
DC is produced to E and AB is produced to G.
So,

D E | | A G

.
Since the rectangle ABCD and the parallelogram ABEF are on the same base AB and between the same parallels,

a r e a (□ A B C D) = a r e a (▱ A B E F)

= A B × A D = 10 × 5 = 50 c m 2

Now, the parallelogram ABEF and

Δ E F G

are on the same base EF and between the same parallels.

⇒ a r e a (Δ E F G) = 12 a r e a (▱ A B E F)

= 12 (50) = 25 c m 2

Area of

Δ E F G = 25 c m 2

.
Hence, option 1) is correct.

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