PSLEThe figure is made up of two rectangles, GHPM and MNKL, and two right-angled isosceles triangles, HJP and KJN. HG = 10 cm, KL = 6 cm and HP =
q cm. GML and JPNM are straight lines.
- Find the length of GL in terms of q. Give your answer in the simplest form.
- Find the total area of the figure when q = 13.
(a)
Length PN
= 10 - 6
= 4 cm
Length JP =
q cm (Isosceles triangle)
Length NK
= Length CG
= (
q + 4) cm (Isosceles triangle)
Length GL
=
q +
q + 4
= (2
q + 4) cm
(b)
Area of Rectangle GHMP
= 13 x 10
= 130 cm
2 Length ML
=
q + 4
= 13 + 4
= 17 cm
Area of Rectangle KLMN
= 17 x 6
= 102 cm
2 Area of Triangle HJP
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle JKN
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 130 + 102 + 84.5 + 144.5
= 461 cm
2 Answer(s): (a) (2
q + 4) cm; b) 461 cm
2