PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 16 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 = 18.
(a)
Length QP
= 16 - 9
= 7 cm
Length KQ =
r cm (Isosceles triangle)
Length PL
= Length CG
= (
r + 7) cm (Isosceles triangle)
Length HM
=
r +
r + 7
= (2
r + 7) cm
(b)
Area of Rectangle HJNQ
= 18 x 16
= 288 cm
2 Length NM
=
r + 7
= 18 + 7
= 25 cm
Area of Rectangle LMNP
= 25 x 9
= 225 cm
2 Area of Triangle JKQ
=
12 x 18 x 18
= 162 cm
2 Area of Triangle KLP
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 288 + 225 + 162 + 312.5
= 987.5 cm
2 Answer(s): (a) (2
r + 7) cm; b) 987.5 cm
2