F.4 Maths trigonometry

1.
(a)
In ΔPRS :
s = (12 + 17 + 25)/2 cm = 27 cm

By Heron's formula :
Area of ΔPRS
= √[27 x (27 - 12) x (27 - 17) x (27 - 25)] cm²
= √(27 x 15 x 10 x 2) cm²
= 90 cm²

(b)
Compare ΔPRS and ΔPQS.
They have the same base (PS) and the same altitude (distance between PS andQR).

Hence, ΔPQS = ΔPRS = 90 cm²

2014-05-03 19:26:30 補充：
It is NOT necessary to prove that they are congruent, but it is only necessary to prove that their areas are equal.

Area of Δ = (1/2) x base x altitude

Area of ΔPRS = (1/2) x PS x (equal altitude)
Area of ΔPQS = (1/2) x PS x (equal altitude)

Hence, ΔPQS = ΔPRS = 90 cm²

can u draw a fig of trapezium-pqrs
ans
(a) 解答
(b) 解答