Question

In the following figure, ABCD, it is given that BC || AD. BC = 10 cm, AD = 6 cm, AB = 5 cm and BE = 3 cm. Find the area of the figure ABCD.

Answer 1

Given: BC || AD, BC = 10 cm, AD = 6 cm, AB = 5 cm, BE = 3 cm.

Step-wise calculation:

1. AE is the perpendicular distance (height) from A to BC.

In right triangle ABE,

`AE = sqrt(AB^2 − BE^2)`

= `sqrt(5^2 - 3^2)`

= `sqrt(25 - 9)`

= `sqrt(16)`

= 4 cm

2. Area of trapezoid ABCD

= `((BC + AD)/2 ) xx "height"` 

= `((10 + 6)/2) xx 4` 

= `(16/2) xx 4`

= 8 × 4

= 32 cm²

Area (ABCD) = 32 cm².