PSLEThe figure is made up of two rectangles, FGNL and LMJK, and two right-angled isosceles triangles, GHN and JHM. GF = 11 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 = 13.
(a)
Length NM
= 11 - 7
= 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
= 13 x 11
= 143 cm
2 Length LK
=
p + 4
= 13 + 4
= 17 cm
Area of Rectangle JKLM
= 17 x 7
= 119 cm
2 Area of Triangle GHN
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle HJM
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 143 + 119 + 84.5 + 144.5
= 491 cm
2 Answer(s): (a) (2
p + 4) cm; b) 491 cm
2