PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 8 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 = 19.
(a)
Length KJ
= 8 - 5
= 3 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 3) cm (Isosceles triangle)
Length CG
=
l +
l + 3
= (2
l + 3) cm
(b)
Area of Rectangle CDHK
= 19 x 8
= 152 cm
2 Length HG
=
l + 3
= 19 + 3
= 22 cm
Area of Rectangle FGHJ
= 22 x 5
= 110 cm
2 Area of Triangle DEK
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle EFJ
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 152 + 110 + 180.5 + 242
= 684.5 cm
2 Answer(s): (a) (2
l + 3) cm; b) 684.5 cm
2