PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 12 cm, HJ = 7 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 = 16.
(a)
Length ML
= 12 - 7
= 5 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 5) cm (Isosceles triangle)
Length EJ
=
n +
n + 5
= (2
n + 5) cm
(b)
Area of Rectangle EFKM
= 16 x 12
= 192 cm
2 Length KJ
=
n + 5
= 16 + 5
= 21 cm
Area of Rectangle HJKL
= 21 x 7
= 147 cm
2 Area of Triangle FGM
=
12 x 16 x 16
= 128 cm
2 Area of Triangle GHL
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 192 + 147 + 128 + 220.5
= 687.5 cm
2 Answer(s): (a) (2
n + 5) cm; b) 687.5 cm
2