PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 12 cm, FG = 6 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 = 15.
(a)
Length KJ
= 12 - 6
= 6 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 6) cm (Isosceles triangle)
Length CG
=
l +
l + 6
= (2
l + 6) cm
(b)
Area of Rectangle CDHK
= 15 x 12
= 180 cm
2 Length HG
=
l + 6
= 15 + 6
= 21 cm
Area of Rectangle FGHJ
= 21 x 6
= 126 cm
2 Area of Triangle DEK
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle EFJ
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 180 + 126 + 112.5 + 220.5
= 639 cm
2 Answer(s): (a) (2
l + 6) cm; b) 639 cm
2