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 = 10.
(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
= 10 x 9
= 90 cm
2 Length HG
=
l + 4
= 10 + 4
= 14 cm
Area of Rectangle FGHJ
= 14 x 5
= 70 cm
2 Area of Triangle DEK
=
12 x 10 x 10
= 50 cm
2 Area of Triangle EFJ
=
12 x 14 x 14
= 98 cm
2 Total area of the figure
= 90 + 70 + 50 + 98
= 308 cm
2 Answer(s): (a) (2
l + 4) cm; b) 308 cm
2