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 = 13.
(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
= 13 x 12
= 156 cm
2 Length LK
=
p + 6
= 13 + 6
= 19 cm
Area of Rectangle JKLM
= 19 x 6
= 114 cm
2 Area of Triangle GHN
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle HJM
=
12 x 19 x 19
= 180.5 cm
2 Total area of the figure
= 156 + 114 + 84.5 + 180.5
= 535 cm
2 Answer(s): (a) (2
p + 6) cm; b) 535 cm
2