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$P Q R S$ is a trapezium having $P S$ is a trapezium having and $Q R$ and as parallel sides. A is any point on $P Q$ as parallel sides. A is any point on and $B$ and is a point on $S R$ is a point on such that $A B | | Q R$ such that . If area of $Δ P B Q$ . If area of is $17 cm 2$ is , then the area of $Δ A S R$ , then the area of from the following choices is:

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17 cm 2

19 cm 2

13 cm 2

15 cm 2

answer is A.

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Detailed Solution

Given that,

P Q R S

is a trapezium having

P S

and

Q R

as parallel sides.
A is any point on

P Q

and

B

is a point on

S R

such that

A B | | Q R

.
The area of

Δ P B Q

17 cm 2

We have to find the area of

Δ A S R

.
We know that, if a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is equal to half the area of the parallelogram.
Area

(Δ APB) =

Area

(Δ ABS)

.........(1)
Area

(Δ AQR) =

Area

(Δ ABR)

.........(2)
Area

(Δ ASR) =

Area

(Δ ABS) +

Area

(Δ ABR)

Substitute value of equation (1) and (2) in the above equation.

Area (Δ ASR) = Area (Δ APB) + Area (Δ AQR) = Area (Δ BPQ) = 17 cm 2

The area of

Δ A S R

17 c m 2

.
Hence option 1) is correct.

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