PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 10 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 = 14.
(a)
Length NM
= 10 - 6
= 4 cm
Length HN =
p cm (Isosceles triangle)
Length MJ
= Length CG
= (
p + 4) cm (Isosceles triangle)
Length FK
=
p +
p + 4
= (2
p + 4) cm
(b)
Area of Rectangle FGLN
= 14 x 10
= 140 cm
2 Length LK
=
p + 4
= 14 + 4
= 18 cm
Area of Rectangle JKLM
= 18 x 6
= 108 cm
2 Area of Triangle GHN
=
12 x 14 x 14
= 98 cm
2 Area of Triangle HJM
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 140 + 108 + 98 + 162
= 508 cm
2 Answer(s): (a) (2
p + 4) cm; b) 508 cm
2