PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 9 cm, FG = 5 cm and DK =
l cm. CHG and EKJH are straight lines.
- Find the length of CG in terms of l. Give your answer in the simplest form.
- Find the total area of the figure when l = 20.
(a)
Length KJ
= 9 - 5
= 4 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 4) cm (Isosceles triangle)
Length CG
=
l +
l + 4
= (2
l + 4) cm
(b)
Area of Rectangle CDHK
= 20 x 9
= 180 cm
2 Length HG
=
l + 4
= 20 + 4
= 24 cm
Area of Rectangle FGHJ
= 24 x 5
= 120 cm
2 Area of Triangle DEK
=
12 x 20 x 20
= 200 cm
2 Area of Triangle EFJ
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 180 + 120 + 200 + 288
= 788 cm
2 Answer(s): (a) (2
l + 4) cm; b) 788 cm
2