PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 10 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 = 12.
(a)
Length KJ
= 10 - 5
= 5 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 5) cm (Isosceles triangle)
Length CG
=
l +
l + 5
= (2
l + 5) cm
(b)
Area of Rectangle CDHK
= 12 x 10
= 120 cm
2 Length HG
=
l + 5
= 12 + 5
= 17 cm
Area of Rectangle FGHJ
= 17 x 5
= 85 cm
2 Area of Triangle DEK
=
12 x 12 x 12
= 72 cm
2 Area of Triangle EFJ
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 120 + 85 + 72 + 144.5
= 421.5 cm
2 Answer(s): (a) (2
l + 5) cm; b) 421.5 cm
2