PSLEThe figure is made up of two rectangles, GHPM and MNKL, and two right-angled isosceles triangles, HJP and KJN. HG = 17 cm, KL = 10 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 = 20.
(a)
Length PN
= 17 - 10
= 7 cm
Length JP =
q cm (Isosceles triangle)
Length NK
= Length CG
= (
q + 7) cm (Isosceles triangle)
Length GL
=
q +
q + 7
= (2
q + 7) cm
(b)
Area of Rectangle GHMP
= 20 x 17
= 340 cm
2 Length ML
=
q + 7
= 20 + 7
= 27 cm
Area of Rectangle KLMN
= 27 x 10
= 270 cm
2 Area of Triangle HJP
=
12 x 20 x 20
= 200 cm
2 Area of Triangle JKN
=
12 x 27 x 27
= 364.5 cm
2 Total area of the figure
= 340 + 270 + 200 + 364.5
= 1174.5 cm
2 Answer(s): (a) (2
q + 7) cm; b) 1174.5 cm
2