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Area of a Triangle

In one line: The area of a triangle is half of its base multiplied by its perpendicular height: Area = ½ × base × height.

Why it works

Area is the amount of flat space a shape covers, measured in square units such as cm² or m². Triangles appear everywhere: roofs, sails, ramps and slices of pizza. Many other shapes can also be split into triangles. Once you can find a triangle's area, you can work out how much paint, fabric or grass seed a job needs, and you can find the area of almost any shape with straight sides.

Think of it like: Imagine a rectangular sandwich cut corner to corner. You get two identical triangles, so each triangle is exactly half the sandwich. The rectangle's area is base × height, so one triangle is ½ × base × height. This works for any triangle with the same base and height, even if it is not a right-angled one. (Where this breaks: The sandwich picture fits neatly only when the triangle has a right angle. For other triangles, the height (the straight up-and-down distance from the base to the top corner) may fall inside or even outside the triangle. For those, think of the triangle as half of a parallelogram (a slanted rectangle) with the same base and height instead.)

Worked example

A triangle has a base of 12 cm, two slanted sides of 10 cm each, and a perpendicular height of 8 cm. What is its area?

  1. Find the base: it is 12 cm.
  2. Find the perpendicular height, meaning the distance from the base to the top corner that meets the base at a right angle: it is 8 cm. Ignore the 10 cm slanted sides.
  3. Multiply base by height: 12 × 8 = 96.
  4. Halve the result: 96 ÷ 2 = 48.
  5. Write the answer in square units because area is measured in squares: 48 cm².

Answer: The area is 48 cm².

Common mistakes

  • Forgetting to halve: base × height gives the area of a whole rectangle, so always divide by 2 at the end.
  • Using a slanted side as the height: the height must meet the base at a right angle, so look for the little square corner symbol or a dotted line.
  • Writing plain units like cm instead of cm²: area counts squares, so always use square units.
  • Mixing units, such as a base in metres and a height in centimetres: convert both to the same unit before multiplying.

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A triangle has a base of 8 cm and a perpendicular height of 6 cm. What is its area?

Questions parents ask

What year do kids learn the area of a triangle?

In the UK, children usually learn the formula in Year 6, and in Australia it is formally taught around Year 7. In the US, it is part of Grade 6. Many children meet the idea of counting squares inside triangles a year or two earlier.

Why do you divide by 2 when finding the area of a triangle?

Any triangle is exactly half of a rectangle or parallelogram with the same base and height. Base × height gives the area of that bigger shape, so dividing by 2 gives the triangle's share.

How can I help my child with area of a triangle at home?

Draw a rectangle on squared paper, cut it along a diagonal and lay the two triangles on top of each other to show they match. Then ask your child to measure triangles around the house, such as a folded napkin, and check that they choose the height at a right angle to the base.

What is the difference between the height and a side of a triangle?

The height is the straight distance from the base to the opposite corner, meeting the base at a right angle. A side is one of the triangle's edges, and it is only the same as the height in a right-angled triangle.