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:
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 × (14cm + 8cm) × 10cm
= ½ × 22cm × 10cm
= 11cm × 10cm
= 110cm2
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