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Area of Rectangles and Triangles

FoundationChallengeAQAEdexcelOCR

Master area of rectangles and triangles for GCSE Maths with structured, exam-style practice. This Foundation resource covers finding the area of rectangles and triangles and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Area of a triangle = ½ × base × height.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

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Topic overview

Area measures the space inside a two-dimensional shape, and it is always given in squared units.

A rectangle's area is length times width. A triangle's is half the base times the perpendicular height, because a triangle is exactly half of the rectangle that encloses it.

The word perpendicular matters. The height must be measured at right angles to the base, not along a sloping side. For an obtuse triangle the perpendicular height may fall outside the shape entirely, and using the slanted side instead is the most common error in the topic.

Revision notes

Rectangles

Area is length multiplied by width, written \(A = lw\).

A rectangle \(9\)cm by \(4\)cm has area \(36\)cm². Both measurements must be in the same units before multiplying.

Triangles

Area is \(\frac{1}{2} \times \text{base} \times \text{perpendicular height}\).

A triangle with base \(10\)cm and height \(6\)cm has area \(\frac{1}{2} \times 10 \times 6 = 30\)cm².

Compound shapes

Split the shape into rectangles and triangles, find each area, then add them.

Alternatively, find the area of a large rectangle and subtract the missing piece. Either approach works provided the working is clear.

Key points

  • Area is measured in squared units.
  • Rectangle area is \(l \times w\).
  • Triangle area is \(\frac{1}{2} \times b \times h\).
  • The height must be perpendicular to the base.
  • Split compound shapes into simpler ones.
  • Convert to the same units before multiplying.

Worked examples

Example 1

Find the area of a rectangle \(11\)cm by \(6\)cm.

Working

\[11 \times 6\]multiply length by width
\[= 66\text{cm}^2\]state the area in squared units

Example 2

Find the area of a triangle with base \(14\)cm and perpendicular height \(5\)cm.

Working

\[\frac{1}{2} \times 14 \times 5\]use the triangle area formula
\[= 35\text{cm}^2\]state the area

Example 3

A compound shape is a \(10\times 6\) rectangle with a \(3\times 2\) rectangle removed. Find its area.

Working

\[10 \times 6 = 60\]find the area of the whole rectangle
\[3 \times 2 = 6\]find the area of the removed piece
\[60 - 6 = 54\text{cm}^2\]subtract to find the remaining area

Common mistakes

  • Using a sloping side as the height.

    The height must be perpendicular to the base, at right angles to it.

  • Forgetting to halve for a triangle.

    A triangle is half the enclosing rectangle, so the ½ is essential.

  • Using ordinary units instead of squared.

    Area is always in cm², m² and so on.

  • Mixing units within a calculation.

    Convert everything to one unit before multiplying.

Exam tips

  • Look for the right-angle marking to identify the perpendicular height.
  • Always include squared units in your answer.
  • Split compound shapes and label each part.
  • Check whether adding or subtracting is the simpler route.

Key terms

Area
The space inside a two-dimensional shape.
Perpendicular height
The height measured at right angles to the base.
Compound shape
A shape made from simpler shapes.
Squared units
Units such as cm² used for area.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.