PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 9 cm, LM = 4 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 = 15.
(a)
Length QP
= 9 - 4
= 5 cm
Length KQ =
r cm (Isosceles triangle)
Length PL
= Length CG
= (
r + 5) cm (Isosceles triangle)
Length HM
=
r +
r + 5
= (2
r + 5) cm
(b)
Area of Rectangle HJNQ
= 15 x 9
= 135 cm
2 Length NM
=
r + 5
= 15 + 5
= 20 cm
Area of Rectangle LMNP
= 20 x 4
= 80 cm
2 Area of Triangle JKQ
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle KLP
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 135 + 80 + 112.5 + 200
= 527.5 cm
2 Answer(s): (a) (2
r + 5) cm; b) 527.5 cm
2