PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 18 cm, HJ = 10 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 = 20.
(a)
Length ML
= 18 - 10
= 8 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 8) cm (Isosceles triangle)
Length EJ
=
n +
n + 8
= (2
n + 8) cm
(b)
Area of Rectangle EFKM
= 20 x 18
= 360 cm
2 Length KJ
=
n + 8
= 20 + 8
= 28 cm
Area of Rectangle HJKL
= 28 x 10
= 280 cm
2 Area of Triangle FGM
=
12 x 20 x 20
= 200 cm
2 Area of Triangle GHL
=
12 x 28 x 28
= 392 cm
2 Total area of the figure
= 360 + 280 + 200 + 392
= 1232 cm
2 Answer(s): (a) (2
n + 8) cm; b) 1232 cm
2