PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 8 cm, FG = 4 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 = 18.
(a)
Length KJ
= 8 - 4
= 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
= 18 x 8
= 144 cm
2 Length HG
=
l + 4
= 18 + 4
= 22 cm
Area of Rectangle FGHJ
= 22 x 4
= 88 cm
2 Area of Triangle DEK
=
12 x 18 x 18
= 162 cm
2 Area of Triangle EFJ
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 144 + 88 + 162 + 242
= 636 cm
2 Answer(s): (a) (2
l + 4) cm; b) 636 cm
2