Formula

Area of a trapezium

Mensuration • Plane Figures • Quadrilateral

Formula

A = \frac{1}{2} (a + b) h

A trapezium whose two parallel sides have lengths

a

and

b

and which are a perpendicular distance

h

apart has area

\frac{1}{2} (a + b) h

How to use it

1Identify the PARALLEL pair first; the other two sides play no part in the formula.
2Read it as the average of the two parallel sides times the height, which makes the rectangle ( $a = b$ ) and the triangle ( $b = 0$ ) the two limiting cases.
3A quadrilateral with one pair of parallel vertical edges in a compound figure is a trapezium on its side — the height is then the horizontal gap.

Worked example

A trapezium has parallel sides

7

cm and

11

cm, which are

4

cm apart. Find its area.

Step-by-step

1
$A = \frac{1}{2} (7 + 11) \times 4$
2
$= \frac{1}{2} \times 18 \times 4 = 36$ cm $^{2}$

Answer

36

^{2}

Watch out

h

is the perpendicular distance between the parallel sides, never the length of a slant side; on an oblique trapezium those differ and using the slant inflates the area.

Also known as

area of a trapezium, area of a trapezoid, half sum of parallel sides times height, parallel sides area formula

Appears in past papers

Formula

Worked example

Appears in past papers

2020 (II)

2020 (I)

2017 (I)