PSLEThe figure is made up of two rectangles, HJQN and NPLM, and two right-angled isosceles triangles, JKQ and LKP. JH = 12 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 = 14.
(a)
Length QP
= 12 - 6
= 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
= 14 x 12
= 168 cm
2 Length NM
=
r + 6
= 14 + 6
= 20 cm
Area of Rectangle LMNP
= 20 x 6
= 120 cm
2 Area of Triangle JKQ
=
12 x 14 x 14
= 98 cm
2 Area of Triangle KLP
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 168 + 120 + 98 + 200
= 586 cm
2 Answer(s): (a) (2
r + 6) cm; b) 586 cm
2