Question

PQRS is a trapezium having PS and QR as parallel sides. A is any point on PQ and B is a point on SR such that AB || QR. If area of $△PBQ$ is 17 cm^2, Find the ara of $△ASR.$

Answer 1

In trapezium PQRS,
PS || QR
A and B are points on sides PQ are SR such that AB || QR
area of $△PBQ=17c{m}^2$

$△ABQand△ABR$ are on the same base AB and between the same parallels
$\therefore ar\left(△ABQ\right)=ar\left(△ABR\right)$
Similarly, $△ABPand△ABS$ are on the same base and between the same parallels
$\therefore ar\left(ABP\right)=ar\left(△ABS\right)Adding\left(i\right)and\left(ii\right)ar\left(ABP\right)=ar\left(△ABP\right)=ar\left(△ABR\right)+ar\left(△ABS\right)\Rightarrow ar\left(△PBQ\right)=ar\left(△ASR\right)$
Put $ar\left(PBQ\right)=17c{m}^2\therefore ar\left(△ASR\right)=17c{m}^2$