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## JSS1: MATHEMATICS - 2ND TERM

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#### Quizzes

Lesson 8, Topic 6
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# Area of a Trapezium

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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