PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 15 cm, LM = 9 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
= 15 - 9
= 6 cm
Length KQ =
r cm (Isosceles triangle)
Length PL
= Length CG
= (
r + 6) cm (Isosceles triangle)
Length HM
=
r +
r + 6
= (2
r + 6) cm
(b)
Area of Rectangle HJNQ
= 20 x 15
= 300 cm
2 Length NM
=
r + 6
= 20 + 6
= 26 cm
Area of Rectangle LMNP
= 26 x 9
= 234 cm
2 Area of Triangle JKQ
=
12 x 20 x 20
= 200 cm
2 Area of Triangle KLP
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 300 + 234 + 200 + 338
= 1072 cm
2 Answer(s): (a) (2
r + 6) cm; b) 1072 cm
2