How to Calculate the Area of a Triangle, Rectangle and Circle

Calculating area is one of the most practical skills in maths. Whether you are working out how much paint to buy for a wall, how much turf to lay in a backyard, or solving geometry questions in a test, the same formulas come up again and again.

This guide covers the three shapes you will use most often: rectangles, triangles and circles. Each section includes the formula, a clear explanation of why it works, and worked examples.

Area of a rectangle

Formula: Area = length × width

This is the most straightforward area formula. A rectangle that is 5 cm long and 3 cm wide can be divided into a grid of 1 cm squares. Count them and you get 15. That is exactly 5 × 3.

Example 1

Find the area of a rectangle with length 8 m and width 4.5 m.

Area = 8 × 4.5 = 36 m²

Example 2

A rectangular room measures 5.2 m by 3.8 m. Find its area.

Area = 5.2 × 3.8 = 19.76 m²

Remember: area is always measured in square units (cm², m², km²). This is because you are multiplying two lengths together.

Squares are just special rectangles where all sides are equal, so Area = side × side = side².

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Area of a triangle

Formula: Area = 1/2 × base × height

Why the half? Picture a rectangle and draw a diagonal from one corner to the opposite corner. You have just split it into two equal triangles. Each triangle is exactly half the rectangle. So the area of a triangle is half the area of the rectangle it fits inside.

The height must be perpendicular (at right angles) to the base. This is the part that trips students up most often. The height is not the slant side of the triangle. It is the vertical distance from the base to the highest point, measured at 90 degrees to the base.

Example 1

Find the area of a triangle with base 10 cm and height 6 cm.

Area = 1/2 × 10 × 6 = 30 cm²

Example 2

Find the area of a triangle with base 7 m and height 3.4 m.

Area = 1/2 × 7 × 3.4 = 1/2 × 23.8 = 11.9 m²

Example 3

A triangular garden bed has a base of 4.5 m and a perpendicular height of 2 m. How much mulch (in m²) is needed to cover it?

Area = 1/2 × 4.5 × 2 = 4.5 m²

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Area of a circle

Formula: Area = π × r²

Here, r is the radius (the distance from the centre to the edge) and π is approximately 3.14159. On most calculators you can use the π button for a more precise value.

A common mistake is using the diameter instead of the radius. The diameter is the full distance across the circle through the centre, which is twice the radius. Always check: if you are given the diameter, halve it first.

Example 1

Find the area of a circle with radius 5 cm.

Area = π × 5² = π × 25 = 78.54 cm² (rounded to 2 decimal places)

Example 2

Find the area of a circle with diameter 12 m.

First, find the radius: r = 12 / 2 = 6 m

Area = π × 6² = π × 36 = 113.10 m² (rounded to 2 decimal places)

Example 3

A circular pond has a radius of 3.5 m. Find its area.

Area = π × 3.5² = π × 12.25 = 38.48 m² (rounded to 2 decimal places)

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Quick reference table

Shape	Formula	Key measurement
Rectangle	length × width	Two adjacent sides
Square	side2	One side
Triangle	1/2 × base × height	Base and perpendicular height
Circle	π × r2	Radius (not diameter)

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Common mistakes to avoid

• Using the slant height for triangles: The height must be perpendicular to the base. If the triangle is not right-angled, the height may need to be drawn inside the triangle as a dotted line.
• Forgetting to halve the diameter: The circle formula uses the radius. If the question gives you a diameter of 10, the radius is 5.
• Missing the square on r: It is π × r², not π × r. Squaring the radius first makes a big difference to the answer.
• Wrong units: If your lengths are in centimetres, your area is in cm². If they are in metres, the area is in m². Never mix units in the same calculation.
• Forgetting to halve for triangles: This one catches students out in tests more than you might expect. Always include that 1/2.

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Combining shapes

In harder problems, you might need to find the area of a shape made up of rectangles, triangles and semicircles joined together. The approach is always the same: break the shape into parts you recognise, find each area separately, then add (or subtract) them.

For example, a shape that looks like a rectangle with a triangle on top can be split into one rectangle and one triangle. Calculate each area and add them together.

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Keep practising

Area calculations are a foundation for surface area, volume, and many real-world measurement problems you will encounter in later years. Getting confident with these three formulas now pays off enormously.

If you want to work through area problems with step-by-step guidance, imSteyn covers measurement and geometry as part of the Year 7 Australian Curriculum. It guides you through the thinking process rather than just giving you the answer, so the formulas start to make sense rather than just being something to memorise.