A trapezium PQRS is such that PQ // RS and the perpendicular P to RS is 40 cm. If |PQ| = 20 cm, |SP| = 50 cm and |SR| = 60 cm. Calculate, correct to 2 significant figures, the
(a) Area of the trapezium ; (b) < QRS.
Explanation
(a) Area of trapezium PQRS = (frac{1}{2}(PQ + RS) times 40)
= (frac{1}{2}(20 + 60) times 40)
= (40 times 40)
= (1600 cm^{2})
(b) In (Delta) SPT,
(|SP|^{2} = |ST|^{2} + |TP|^{2}) (Pythagoras theorem)
(|ST|^{2} = |SP|^{2} – |TP|^{2})
= (50^{2} – 40^{2})
= (2500 – 1600)
(|ST|^{2} = 900)
(therefore |ST| = 30 cm)
(|UR| = 60 cm – (30 + 20) cm)
= 10 cm
Let < QRS = (alpha),
(tan alpha = frac{40}{10} = 4)
(alpha = tan^{-1} (4))
= (75.96° approxeq 76°)