G2GeometryFoundation

Area & Perimeter

Perimeter is the distance all the way around a shape; area is the space inside it. Learn the area formulas for the basic shapes and you can break any compound shape into pieces.

35 min Video by Maths Genie AQA GCSE Maths

Area of Compound ShapesWatch the walkthrough, then read the notes below.

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What you'll learn

Find the perimeter of 2D shapes
Use area formulas for rectangles, triangles and parallelograms
Find the area of a trapezium
Find the area of compound shapes

Area formulas

Rectangle: length × width. Triangle: $\frac{1}{2} \times$ base × height. Parallelogram: base × height. Trapezium: $\frac{1}{2} (a + b) \times h$ .

triangle = \frac{1}{2} bh

Half base times height.

trapezium = \frac{1}{2} (a + b) h

a and b are the parallel sides.

Compound shapes

Split a compound shape into rectangles and triangles, find each area, then add them up. Areas use square units (cm², m²).

\frac{1}{2} \times 8 \times 5

= 20

cm².

Answer20 cm²

Tip — Area is in square units; perimeter is in ordinary length units.

Remember these

rectangle = l \times w

Length × width.

triangle = \frac{1}{2} bh

Half base × height.

trapezium = \frac{1}{2} (a + b) h

Parallel sides a, b.

Watch out for these

Forgetting the ½ in the triangle area.

Area of a triangle is ½ × base × height.

Giving area in cm instead of cm².

Area always uses square units.

Key takeaways

Perimeter = distance around; area = space inside (square units).
Triangle = ½bh; trapezium = ½(a+b)h.
Split compound shapes into simple ones and add.

Test yourself

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