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 = 16.
(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
= 16 x 12
= 192 cm
2 Length HG
=
l + 5
= 16 + 5
= 21 cm
Area of Rectangle FGHJ
= 21 x 7
= 147 cm
2 Area of Triangle DEK
=
12 x 16 x 16
= 128 cm
2 Area of Triangle EFJ
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 192 + 147 + 128 + 220.5
= 687.5 cm
2 Answer(s): (a) (2
l + 5) cm; b) 687.5 cm
2