PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 12 cm, FG = 7 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 = 13.
(a)
Length KJ
= 12 - 7
= 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
= 13 x 12
= 156 cm
2 Length HG
=
l + 5
= 13 + 5
= 18 cm
Area of Rectangle FGHJ
= 18 x 7
= 126 cm
2 Area of Triangle DEK
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle EFJ
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 156 + 126 + 84.5 + 162
= 528.5 cm
2 Answer(s): (a) (2
l + 5) cm; b) 528.5 cm
2