Question

A piece of land ABCD is in the shape of a trapezium

as shown in the diagram. AB = 40 m, BC = 39 m,
AD = 30 m, and <ABC = <BAD = 90°. Find
(a) the length of the side CD,
(b) angle BCD,
(c) the area of the land.
​

Answer 1

a) CD = 41 m

b) 77.32°

c) 1380 square metres

Explanation:

We can divide the trapezium as shown in the diagram below.

a) To find CD, we use Pythagoras Rule:

`CD^2 = 9^2 + 40^2`

`CD^2 = 81 + 1600\\\\CD^2 = 1681\\\\=> CD = 41 m`

b) To find <BCD, we use trigonometric function SOHCAHTOA:

sin(BCD) = opp / hyp

sin(BCD) = 40 / 41

sin(BCD) = 0.9756

=> <BCD = 77.32°

c) The area of a trapezium is given as:

A = 1/2 (a + b) * h

where h = height = 40 m

a = top length = 30 m

b = bottom length = 39 m

A = 1/2 * (30 + 39) * 40

A = 1/2 * 69 * 40

A = 1380 square metres