Perimeters And Areas Of Plane Figures — Important Questions

60 cm²

Step 1: Given base = 10 cm, height = 6 cm. Step 2: Apply area formula for parallelogram: A = base × height. Step 3: Substitute values: A = 10 × 6. Step 4: Calculate: A = 60 cm². The height must be perpendicular to the base.

96 cm²

Step 1: Given diagonals d₁ = 16 cm and d₂ = 12 cm. Step 2: Apply area formula for rhombus: A = (1/2) × d₁ × d₂. Step 3: Substitute values: A = (1/2) × 16 × 12. Step 4: Calculate: A = (1/2) × 192 = 96 cm². Diagonals of rhombus bisect each other at right angles.

96 cm²

Step 1: Given parallel sides a = 15 cm, b = 9 cm, height h = 8 cm. Step 2: Apply trapezium area formula: A = (1/2)(a + b) × h. Step 3: Substitute values: A = (1/2)(15 + 9) × 8 = (1/2) × 24 × 8. Step 4: Calculate: A = 96 cm². The formula averages the parallel sides and multiplies by height.

25.67 cm²

Step 1: Given radius = 7 cm, angle θ = 60°, π = 22/7. Step 2: Apply sector area formula: A = (πr²θ)/360°. Step 3: Substitute: A = [(22/7) × 49 × 60]/360 = (22 × 49 × 60)/(7 × 360). Step 4: Calculate: A = 64680/2520 = 25.67 cm². Sector is a portion of circle bounded by two radii.