PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 12 cm, JK = 7 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 = 16.
(a)
Length NM
= 12 - 7
= 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
= 16 x 12
= 192 cm
2 Length LK
=
p + 5
= 16 + 5
= 21 cm
Area of Rectangle JKLM
= 21 x 7
= 147 cm
2 Area of Triangle GHN
=
12 x 16 x 16
= 128 cm
2 Area of Triangle HJM
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 192 + 147 + 128 + 220.5
= 687.5 cm
2 Answer(s): (a) (2
p + 5) cm; b) 687.5 cm
2