PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 7 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 = 18.
(a)
Length ML
= 7 - 4
= 3 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 3) cm (Isosceles triangle)
Length EJ
=
n +
n + 3
= (2
n + 3) cm
(b)
Area of Rectangle EFKM
= 18 x 7
= 126 cm
2 Length KJ
=
n + 3
= 18 + 3
= 21 cm
Area of Rectangle HJKL
= 21 x 4
= 84 cm
2 Area of Triangle FGM
=
12 x 18 x 18
= 162 cm
2 Area of Triangle GHL
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 126 + 84 + 162 + 220.5
= 592.5 cm
2 Answer(s): (a) (2
n + 3) cm; b) 592.5 cm
2