Question

In the parallelogram PQRS shown, if A is a point on the side RS, then area of parallelogram is _____times the sum of areas of ΔQRA and ΔSAP.

• A. 2
• B. 3
• C. 4
• D. 1.5

Answer 1

The correct option is A 2

Triangle QAP and parallelogram PQRS are on the same base and between the same parallels.

So, Area ΔQAP = $\frac{1}{2}$ Area of PQRS...(i)

Area ΔQRA + Area ΔSAP + Area ΔQAP = Area of PQRS

Area ΔQRA + Area ΔSAP + $\frac{1}{2}$ Area of PQRS = Area of PQRS...from(i)

Area ΔQRA + Area ΔSAP = $\frac{1}{2}$ Area of PQRS

$\therefore$Area of PQRS
= 2 × (Area of ΔQRA + Area of ΔSAP)