Question

PQRS and ABRS are parallelogram lying on same base X is any point on side BR show that area of(AXS)is equal to half of area of (PQRS )

Answer 1

I hope that's your answer

Answer 2

GIVEN THAT:-

PQRS and ABRS are parallelograms and X is any point on BR.

TO PROVE:-

(i) A(PQRS) = A(ABRS)

(ii) $\small\tt{A(AXS)=\frac{1}{2}(PQRS)}$

PROOF:-

(i) Since, ||gm PQRS and ABRS are on the same base RS and between same parallels RS and PB.

$\therefore$$\small\tt{A(PQRS)=A(ABRS)}$.......(1)

(ii) Since, AXS and ||gm ABRS are on the same base AS between the same parallels AS and BR.

$\therefore$$\large\tt{A(∆AXS)=\frac{1}{2}A(ABRS)}$

$\large\tt\red{A(∆AXS)=\frac{1}{2}A(PQRS)}$