In the diagram, ABCD is a trapezium in which (AD parallel BC) and (< ABC) is a right angle. If |AD| = 15 cm, |BD| = 17 cm and |BC| = 9 cm, calculate :
(a) |AB| ;
(b) the area of the triangle BCD ;
(c) |CD| ;
(d) perimeter of the trapezium.
Explanation
(a) (|AB| = sqrt{|BD|^{2} – |AD|^{2}})
= (sqrt{17^{2} – 15^{2}} = sqrt{289 – 225})
= (sqrt{64} = 8 cm)
(b) Area of triangle BCD = (frac{1}{2} times 9 times 8 )
= (36 cm^{2})
(c) (|EC| = 6 cm)
(|CD| = sqrt{8^{2} + 6^{2}} = sqrt{100})
= 10 cm.
(d) Perimeter of the trapezium = 15 cm + 8 cm + 9 cm + 10 cm
= 42 cm.