Which height is used in the area formula for a triangle?

the perpendicular height. It is measured at right angles to the base.

Area and perimeter · Cambridge IGCSE Mathematics revision

In plain words

Perimeter is the distance round the edge: fencing. Area is the space inside: carpet. They are different things with different units, and each shape has its own formula for area.

Three things to know

Rectangle: length × width. Triangle: ½ × base × height. Parallelogram: base × height.
Trapezium: ½ × (sum of the parallel sides) × the distance between them.
The height in every formula is the perpendicular height, straight up from the base, not a sloping side. For a compound shape, split it into simpler shapes.

Worked example

Find the area of a trapezium with parallel sides of 6 cm and 10 cm that are 4 cm apart.

Area = ½ × (a + b) × h.
= ½ × (6 + 10) × 4 = ½ × 16 × 4.
= 32 cm².

Tips and tricks

Perimeter is in cm; area is in cm². Getting the unit right is often a mark.
Don't forget the ½ for triangles and trapeziums.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Area and perimeter: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the area of a rectangle 7 cm by 4 cm?
- 11 cm²
- 22 cm²
- 28 cm² (the answer)
- 14 cm²
7 × 4.
What is the area of a triangle with base 10 cm and height 6 cm?
- 16 cm²
- 30 cm² (the answer)
- 60 cm²
- 8 cm²
½ × 10 × 6.
What is the perimeter of a square with sides of 5 cm?
- 10 cm
- 20 cm (the answer)
- 25 cm
- 15 cm
4 × 5.
What is the area of a trapezium with parallel sides 4 cm and 8 cm, 5 cm apart?
- 160 cm²
- 60 cm²
- 30 cm² (the answer)
- 17 cm²
½ × 12 × 5.
Which height is used in the area formula for a triangle?
- the longest side
- a sloping side
- the perpendicular height (the answer)
- half the base
It is measured at right angles to the base.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 6 marks. Write your answers on paper, then check them.