Question

A wall is in the shape of a trapezium whose parallel sides are 50 m and 20 m. The non-parallel sides are 28 m and 26 m. Find the area of the wall.
[4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Draw a line CE parallel to AD and draw a perpendicular CF on AB.

It can be observed that AECD is a parallelogram.

CE = AD = 26 m

AE = DC = 50 m

BE = 50 − AB = 50m - 20 m = 30m

For $\Delta BEC$,

s = $\frac{Perimeter}{2}$= $\frac{(26+28+30)}{2}$ =42cm

Area of the $\Delta BEC$ = $\sqrt{s(s-a)(s-b)(s-c)}$ = $\sqrt{42(42-26)(42-28)(42-30)}$ = 336 ${cm}^2$

Now, area of $\Delta BEC$ = $\frac{1}{2}\times base\times height$= $\frac{1}{2}\times BE\times CF$= $\frac{1}{2}\times 30\times CF$

CF= $\frac{672}{30}$ = 22.4cm

Area of AECD = CF $\times$ AE = 22.4 $\times$ 50 = 1120 ${cm}^2$

Therefore, the area of wall = 1120 - 336 = 784 ${cm}^2$.