PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 12 cm, HJ = 6 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 = 15.
(a)
Length ML
= 12 - 6
= 6 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 6) cm (Isosceles triangle)
Length EJ
=
n +
n + 6
= (2
n + 6) cm
(b)
Area of Rectangle EFKM
= 15 x 12
= 180 cm
2 Length KJ
=
n + 6
= 15 + 6
= 21 cm
Area of Rectangle HJKL
= 21 x 6
= 126 cm
2 Area of Triangle FGM
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle GHL
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 180 + 126 + 112.5 + 220.5
= 639 cm
2 Answer(s): (a) (2
n + 6) cm; b) 639 cm
2