PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 12 cm, FG = 6 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 = 14.
(a)
Length KJ
= 12 - 6
= 6 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 6) cm (Isosceles triangle)
Length CG
=
l +
l + 6
= (2
l + 6) cm
(b)
Area of Rectangle CDHK
= 14 x 12
= 168 cm
2 Length HG
=
l + 6
= 14 + 6
= 20 cm
Area of Rectangle FGHJ
= 20 x 6
= 120 cm
2 Area of Triangle DEK
=
12 x 14 x 14
= 98 cm
2 Area of Triangle EFJ
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 168 + 120 + 98 + 200
= 586 cm
2 Answer(s): (a) (2
l + 6) cm; b) 586 cm
2