PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 8 cm, HJ = 4 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 = 11.
(a)
Length ML
= 8 - 4
= 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
= 11 x 8
= 88 cm
2 Length KJ
=
n + 4
= 11 + 4
= 15 cm
Area of Rectangle HJKL
= 15 x 4
= 60 cm
2 Area of Triangle FGM
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle GHL
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 88 + 60 + 60.5 + 112.5
= 321 cm
2 Answer(s): (a) (2
n + 4) cm; b) 321 cm
2