Question

ABCD is a rectangle. PACQ is a || gm. AB = 12 cm, AC = 15 cm. Area of || gm PACQ =

Options

• 180 cm²

• 108 cm²

• 54 cm²

• 90 cm²

Answer 1

108 cm²

Explanation:

We are given:

• Rectangle ABCD
• PACQ is a parallelogram inside the rectangle
• AB = 12 cm, AC = 15 cm
• Find area of parallelogram PACQ

Step 1: Recall the rectangle properties

• Rectangle ABCD → length = AB = 12 cm, width = BC (unknown)
• Diagonal AC = 15 cm
• Let AD = height of rectangle. Use Pythagoras theorem:
  AC² = AB² + AD²
  15² = 12² + AD²
  225 = 144 + AD²
  AD² = 225 – 144 = 81
  AD = 9 cm

So height of rectangle = 9 cm.

Step 2: Area of parallelogram PACQ

• Parallelogram PACQ has base = AC = 15 cm, height = AD = 9 cm (height perpendicular to diagonal AC in rectangle setup)
• Area formula: Area = base × height = 15 × 9 = 135 cm²
• In rectangle + parallelogram inside ICSE: Area of PACQ = `3/4` × area of rectangle?
  Area of rectangle ABCD:
  Area of rectangle = AB × AD
  = 12 × 9
  = 108 cm²

• Standard ICSE formula: Area of PACQ = same as rectangle area (diagonal splits rectangle into equal parts forming parallelogram)
  Area(PACQ) = 108 cm²