Areas of Basic Shapes

A number of expressions are available to calculate the area of a region defined by a basic shape, as shown in the illustration above, and summarised in the table below.

Shape Area Shape Area Shape Area
Square Equation: A = s^2 Trapezoid Equation: A = (a + b) / 2 × h Ellipse Equation: A = π × a × b
Rectangle /

Parallelogram
Equation: A = b × h Triangle Equation: A = 1 / 2 × b × h Circle Equation: A = π × r^2

The basic approach is to:

  1. Identify the shape, and the appropriatete equation.
  2. Find all required parameters (width, height, radius, etc.).
  3. Convert all lengths to the chosen unit, if necessary.
  4. Calculate the area and remember to add the appropriate unit of area (unit2).

Worked Example 1

Find the area of a triangle with a base width of 1.4 m and a height perpendicular to the base of 0.4 m. Give your answer in square metres.
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b = 1.4 m and h = 0.4 m

A = 1 / 2 × b × h

  = 0.5 × 1.4 × 0.4

  = 0.28 m2

Worked Example 2

Find the area of a circle of radius 4 cm. Give your answer in cm2.
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A = π × r2

  = π × 42

  = 50.27 cm2 to 2 d.p.

Worked Example 3

Find the area of a rectangle with a base of 80 cm and a height of 50 cm. Give your answer in m2.
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The answer needs to be in m2 so begin by converting all lengths to metres.

b = 0.8 m, h = 0.5 m

A = b × h

  = 0.8 × 0.5

  = 0.4 m2

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