WAEC Mathematics 1999 Theory question 104

Theory question 104

Mensuration of Plane Shapes

In the diagram, ABCD is a trapezium in which AD//BC and ∠ABC is a right angle. If |AD| = 15cm, |BD| = 17cm and |BC| = 9cm, calculate (a) |AB|. (b) the area of the triangle BCD. (c) |CD|. (d) the perimeter of the trapezium.

Show the model answer

Model answer

(a) ∠BAD = 90° (AD ∥ BC), so AB = √(17² − 15²) = √64 = 8 cm.
(b) Area BCD = ½ × BC × AB = ½ × 9 × 8 = 36 cm².
(c) Drop a perpendicular from C to AD: horizontal gap = 15 − 9 = 6 cm, height 8 cm, so CD = √(6² + 8²) = 10 cm.
(d) Perimeter = 15 + 8 + 9 + 10 = 42 cm.

Explanation

The height of triangle BCD on base BC is the trapezium's height AB.