PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 15 cm, FG = 8 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
= 15 - 8
= 7 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 7) cm (Isosceles triangle)
Length CG
=
l +
l + 7
= (2
l + 7) cm
(b)
Area of Rectangle CDHK
= 18 x 15
= 270 cm
2 Length HG
=
l + 7
= 18 + 7
= 25 cm
Area of Rectangle FGHJ
= 25 x 8
= 200 cm
2 Area of Triangle DEK
=
12 x 18 x 18
= 162 cm
2 Area of Triangle EFJ
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 270 + 200 + 162 + 312.5
= 944.5 cm
2 Answer(s): (a) (2
l + 7) cm; b) 944.5 cm
2