Measuring Space: Perimeter and Area

Find the area of any triangle from its three sides with Heron’s formula, and of a quadrilateral by splitting it into triangles.

Key ideas

• The perimeter is the sum of the sides; the semi-perimeter s is half of it.
• Heron’s formula needs only the three sides, no height.
• Check that the sides make a triangle: each side is less than the sum of the other two.
• For a quadrilateral, draw a diagonal to split it into two triangles and add their areas.
• Keep all sides in the same unit; the area comes out in square units.

Remember

Watch out

• Using the full perimeter in place of s.
• Mixing units, such as metres and centimetres, in one calculation.
• Forgetting the square root, or writing the answer in m instead of m².

Worked example