PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 9 cm, JK = 4 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 = 10.
(a)
Length NM
= 9 - 4
= 5 cm
Length HN =
p cm (Isosceles triangle)
Length MJ
= Length CG
= (
p + 5) cm (Isosceles triangle)
Length FK
=
p +
p + 5
= (2
p + 5) cm
(b)
Area of Rectangle FGLN
= 10 x 9
= 90 cm
2 Length LK
=
p + 5
= 10 + 5
= 15 cm
Area of Rectangle JKLM
= 15 x 4
= 60 cm
2 Area of Triangle GHN
=
12 x 10 x 10
= 50 cm
2 Area of Triangle HJM
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 90 + 60 + 50 + 112.5
= 312.5 cm
2 Answer(s): (a) (2
p + 5) cm; b) 312.5 cm
2