PSLEThe figure is made up of two rectangles, GHPM and MNKL, and two right-angled isosceles triangles, HJP and KJN. HG = 8 cm, KL = 4 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 = 19.
(a)
Length PN
= 8 - 4
= 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
= 19 x 8
= 152 cm
2 Length ML
=
q + 4
= 19 + 4
= 23 cm
Area of Rectangle KLMN
= 23 x 4
= 92 cm
2 Area of Triangle HJP
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle JKN
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 152 + 92 + 180.5 + 264.5
= 689 cm
2 Answer(s): (a) (2
q + 4) cm; b) 689 cm
2