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 = 12.
(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
= 12 x 8
= 96 cm
2 Length HG
=
l + 4
= 12 + 4
= 16 cm
Area of Rectangle FGHJ
= 16 x 4
= 64 cm
2 Area of Triangle DEK
=
12 x 12 x 12
= 72 cm
2 Area of Triangle EFJ
=
12 x 16 x 16
= 128 cm
2 Total area of the figure
= 96 + 64 + 72 + 128
= 360 cm
2 Answer(s): (a) (2
l + 4) cm; b) 360 cm
2