Question

PQRS is a rectangle and AQRB is a || gm, SR = 9 cm, PS = 12 cm

Area of || gm AQRB =

Options

• 2 area of ΔBSR

• 2 area of ΔPAQ

• 108 cm²

• 144 cm²

Answer 1

108 cm²

Explanation:

We are given:

• Rectangle PQRS with PS = 12 cm, SR = 9 cm
• AQRB is a parallelogram inside the rectangle
• We are to find area of ΔCQR

Step 1: Area of rectangle

Area of rectangle PQRS = length × breadth

= PS × SR

= 12 × 9

= 108 cm²

Step 2: Observation about the triangle ΔCQR

• In rectangle PQRS, diagonal divides rectangle into two congruent triangles. 
• Therefore, any triangle formed using one diagonal as base and opposite vertex as apex has area equal to half of rectangle if it covers the full base and height.
• However, in the ICSE setup with parallelogram AQRB, ΔCQR is the triangle formed between the corner C and two vertices of the parallelogram lying on the rectangle’s sides. 
• By geometric properties in ICSE rectangle + parallelogram problems, area of ΔCQR = area of the rectangle.

Area of ΔCQR = 108 cm²