Question

Here is a figure of a playground of trapezium-shaped. Find the area of the playground.

[4 marks]

Answer 1

Area of trapezium ABCD = Area of ADE + Area of Rectangle DEFC + Area of CFB
$=$ ( $\frac{1}{2}\times h\times c)$$+$$(b\times h)$ $+$ ($\frac{1}{2}\times h\times d$)
[1 mark]
$=h\times [\frac{1}{2}\times c+b+\frac{1}{2}\times d]$ $=h\times \left[\frac{c+2\times b+d}{2}\right]$
$=h\times \left[\frac{c+b+d+b}{2}\right]$
$=h\times \left[\frac{a+b}{2}\right]$ $\because (c+b+d=a)$
[2 mark]
$So,wecanwritetheformulafortheareaofatrapezium$
$=height\times \left[\frac{sumofparallelsides}{2}\right]$ $=\frac{1}{2}\times [distancebetweentwoparallelsides\times (sumofparallelsides\left)\right]$
[1 mark]