PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 12 cm, JK = 6 cm and GN =
p cm. FLK and HNML are straight lines.
- Find the length of FK in terms of p. Give your answer in the simplest form.
- Find the total area of the figure when p = 20.
(a)
Length NM
= 12 - 6
= 6 cm
Length HN =
p cm (Isosceles triangle)
Length MJ
= Length CG
= (
p + 6) cm (Isosceles triangle)
Length FK
=
p +
p + 6
= (2
p + 6) cm
(b)
Area of Rectangle FGLN
= 20 x 12
= 240 cm
2 Length LK
=
p + 6
= 20 + 6
= 26 cm
Area of Rectangle JKLM
= 26 x 6
= 156 cm
2 Area of Triangle GHN
=
12 x 20 x 20
= 200 cm
2 Area of Triangle HJM
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 240 + 156 + 200 + 338
= 934 cm
2 Answer(s): (a) (2
p + 6) cm; b) 934 cm
2