PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 8 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 = 13.
(a)
Length ML
= 8 - 4
= 4 cm
Length GM =
n cm (Isosceles triangle)
Length LH
= Length CG
= (
n + 4) cm (Isosceles triangle)
Length EJ
=
n +
n + 4
= (2
n + 4) cm
(b)
Area of Rectangle EFKM
= 13 x 8
= 104 cm
2 Length KJ
=
n + 4
= 13 + 4
= 17 cm
Area of Rectangle HJKL
= 17 x 4
= 68 cm
2 Area of Triangle FGM
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle GHL
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 104 + 68 + 84.5 + 144.5
= 401 cm
2 Answer(s): (a) (2
n + 4) cm; b) 401 cm
2