Area of a Trapezium

A trapezium is a four-sided shape with one pair of opposite sides parallel. The height (h) of a trapezium is the perpendicular distance between the two parallel sides.

Area of ΔACD = \( \frac{1}{2} \scriptsize ah \)

For ΔABC, the base is AB  (i.e. b) and the height to side AB is also equal to h.

Area of ΔABC = \( \frac{1}{2} \scriptsize bh \)

Therefore, the area of trapezium ABCD  =  Areas of  ΔACD  and   ΔABC

= \(\normalsize \frac{1}{2} \scriptsize ah \: + \: \normalsize \frac{1}{2} \scriptsize bh \)

= \(\normalsize \frac{1}{2} \scriptsize h(a \: + \: b)\)

Area of a trapezium  = \(\normalsize \frac{1}{2} \scriptsize (a \: + \: b)h\)

Example 8.6.1:

Calculate the area of a trapezium with the dimensions shown in the figure below:

Solution:

Area of a trapezium = ½  ×  (sum of parallel sides)  ×  height

= ½  ×  (14 cm  +  8 cm)  ×  10 cm

= ½  ×  22 cm  ×  10 cm

= 11 cm  ×  10 cm

= 110 cm²