PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 15 cm, HJ = 8 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
= 15 - 8
= 7 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 7) cm (Isosceles triangle)
Length EJ
=
n +
n + 7
= (2
n + 7) cm
(b)
Area of Rectangle EFKM
= 20 x 15
= 300 cm
2 Length KJ
=
n + 7
= 20 + 7
= 27 cm
Area of Rectangle HJKL
= 27 x 8
= 216 cm
2 Area of Triangle FGM
=
12 x 20 x 20
= 200 cm
2 Area of Triangle GHL
=
12 x 27 x 27
= 364.5 cm
2 Total area of the figure
= 300 + 216 + 200 + 364.5
= 1080.5 cm
2 Answer(s): (a) (2
n + 7) cm; b) 1080.5 cm
2