Area

Overview

This chapter covers area and mensuration of plane figures — triangles, parallelograms, trapeziums, rhombuses and circles — and the surface area of simple solids. Area measures the region a shape covers.

Key concepts

• Area is measured in square units such as cm² and m².
• A composite figure can be split into known shapes and the areas added.
• A trapezium area uses the average of the two parallel sides.
• Surface area of a solid is the total area of all its faces.

Important formulae

• Triangle = (1 ÷ 2) × base × height; Parallelogram = base × height.
• Trapezium = (1 ÷ 2) × (a + b) × height; Rhombus = (1 ÷ 2) × d₁ × d₂.
• Circle area = π r²; circumference = 2 π r.

Solved example

1. Find the area of a trapezium with parallel sides 12 cm and 8 cm and height 5 cm.
2. Area = (1 ÷ 2) × (12 + 8) × 5.
3. = (1 ÷ 2) × 20 × 5 = 50 cm².

Important questions

1. Find the area of a rhombus whose diagonals are 10 cm and 24 cm.
2. A circle has radius 7 cm. Find its area (take π = 22 ÷ 7).
3. Find the area of a triangle with base 14 cm and height 9 cm.
4. A floor 6 m by 4 m is tiled with 50 cm square tiles. How many tiles are needed?

Quick revision

Pick the right formula for each shape and keep units consistent (square units). Break composite shapes into simple parts. For trapezium use the average of parallel sides; for rhombus use half the product of diagonals.