PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 11 cm, LM = 6 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 = 12.
(a)
Length QP
= 11 - 6
= 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
= 12 x 11
= 132 cm
2 Length NM
=
r + 5
= 12 + 5
= 17 cm
Area of Rectangle LMNP
= 17 x 6
= 102 cm
2 Area of Triangle JKQ
=
12 x 12 x 12
= 72 cm
2 Area of Triangle KLP
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 132 + 102 + 72 + 144.5
= 450.5 cm
2 Answer(s): (a) (2
r + 5) cm; b) 450.5 cm
2