PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 9 cm, LM = 5 cm and JQ =
r cm. HNM and KQPN are straight lines.
- Find the length of HM in terms of r. Give your answer in the simplest form.
- Find the total area of the figure when r = 20.
(a)
Length QP
= 9 - 5
= 4 cm
Length KQ =
r cm (Isosceles triangle)
Length PL
= Length CG
= (
r + 4) cm (Isosceles triangle)
Length HM
=
r +
r + 4
= (2
r + 4) cm
(b)
Area of Rectangle HJNQ
= 20 x 9
= 180 cm
2 Length NM
=
r + 4
= 20 + 4
= 24 cm
Area of Rectangle LMNP
= 24 x 5
= 120 cm
2 Area of Triangle JKQ
=
12 x 20 x 20
= 200 cm
2 Area of Triangle KLP
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 180 + 120 + 200 + 288
= 788 cm
2 Answer(s): (a) (2
r + 4) cm; b) 788 cm
2