PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 9 cm, HJ = 5 cm and FM =
n cm. EKJ and GMLK are straight lines.
- Find the length of EJ in terms of n. Give your answer in the simplest form.
- Find the total area of the figure when n = 18.
(a)
Length ML
= 9 - 5
= 4 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 4) cm (Isosceles triangle)
Length EJ
=
n +
n + 4
= (2
n + 4) cm
(b)
Area of Rectangle EFKM
= 18 x 9
= 162 cm
2 Length KJ
=
n + 4
= 18 + 4
= 22 cm
Area of Rectangle HJKL
= 22 x 5
= 110 cm
2 Area of Triangle FGM
=
12 x 18 x 18
= 162 cm
2 Area of Triangle GHL
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 162 + 110 + 162 + 242
= 676 cm
2 Answer(s): (a) (2
n + 4) cm; b) 676 cm
2