PSLEThe figure is made up of two rectangles, CDKH and HJFG, and two right-angled isosceles triangles, DEK and FEJ. DC = 15 cm, FG = 8 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
= 15 - 8
= 7 cm
Length EK =
l cm (Isosceles triangle)
Length JF
= Length CG
= (
l + 7) cm (Isosceles triangle)
Length CG
=
l +
l + 7
= (2
l + 7) cm
(b)
Area of Rectangle CDHK
= 16 x 15
= 240 cm
2 Length HG
=
l + 7
= 16 + 7
= 23 cm
Area of Rectangle FGHJ
= 23 x 8
= 184 cm
2 Area of Triangle DEK
=
12 x 16 x 16
= 128 cm
2 Area of Triangle EFJ
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 240 + 184 + 128 + 264.5
= 816.5 cm
2 Answer(s): (a) (2
l + 7) cm; b) 816.5 cm
2