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Area of rectangles and triangles

Years 4 to 9

Area is the space inside a shape. A rectangle is length × width, and a triangle is half of that.

64rectangle = 6 × 4 = 2446triangle = ½ × 6 × 4 = 12A triangle is half of the rectangle around it.
A 6 by 4 rectangle has area 24. The triangle with base 6 and height 4 is half of it, so 12.

For learners

Area tells you how much flat space a shape covers. We count it in square units, such as cm².

For a rectangle, multiply the length by the width. A rectangle 6 cm long and 4 cm wide has an area of 6 × 4 = 24 cm².

A triangle is half a rectangle. Multiply the base by the height, then halve it. A triangle with base 6 cm and height 4 cm has an area of 12 cm².

A worked example

Find the area of a triangle with base 10 cm and height 7 cm.

  1. Base × height = 10 × 7 = 70.
  2. Half of 70 is 35.
  3. The area is 35 cm².

For grown-ups

Cover a rectangle with square tiles first, so the rule 'rows × columns' is seen before it is used. For triangles, cut a rectangle along its diagonal and show both halves are the same. The height must be the straight-up distance, not the slanted side.

Common mistakes

  • Using the slanted side instead of the straight-up height.
  • Forgetting to halve for a triangle.
  • Writing cm instead of cm² for area.

Why it matters

Builders, gardeners and designers all need area to buy paint, turf or flooring.

Topics in quarter that use this

  • Perimeter and area
  • Area of triangles and trapeziums
  • Area of a parallelogram
  • Area of compound shapes
  • Area by counting squares

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