PSLEThe figure is made up of two rectangles, GHPM and MNKL, and two right-angled isosceles triangles, HJP and KJN. HG = 12 cm, KL = 7 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
= 12 - 7
= 5 cm
Length JP =
q cm (Isosceles triangle)
Length NK
= Length CG
= (
q + 5) cm (Isosceles triangle)
Length GL
=
q +
q + 5
= (2
q + 5) cm
(b)
Area of Rectangle GHMP
= 19 x 12
= 228 cm
2 Length ML
=
q + 5
= 19 + 5
= 24 cm
Area of Rectangle KLMN
= 24 x 7
= 168 cm
2 Area of Triangle HJP
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle JKN
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 228 + 168 + 180.5 + 288
= 864.5 cm
2 Answer(s): (a) (2
q + 5) cm; b) 864.5 cm
2