PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 14 cm, JK = 8 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 = 17.
(a)
Length NM
= 14 - 8
= 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
= 17 x 14
= 238 cm
2 Length LK
=
p + 6
= 17 + 6
= 23 cm
Area of Rectangle JKLM
= 23 x 8
= 184 cm
2 Area of Triangle GHN
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle HJM
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 238 + 184 + 144.5 + 264.5
= 831 cm
2 Answer(s): (a) (2
p + 6) cm; b) 831 cm
2