PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 11 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 = 19.
(a)
Length KJ
= 11 - 6
= 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
= 19 x 11
= 209 cm
2 Length HG
=
l + 5
= 19 + 5
= 24 cm
Area of Rectangle FGHJ
= 24 x 6
= 144 cm
2 Area of Triangle DEK
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle EFJ
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 209 + 144 + 180.5 + 288
= 821.5 cm
2 Answer(s): (a) (2
l + 5) cm; b) 821.5 cm
2