PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 15 cm, HJ = 9 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
= 15 - 9
= 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
= 18 x 15
= 270 cm
2 Length KJ
=
n + 6
= 18 + 6
= 24 cm
Area of Rectangle HJKL
= 24 x 9
= 216 cm
2 Area of Triangle FGM
=
12 x 18 x 18
= 162 cm
2 Area of Triangle GHL
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 270 + 216 + 162 + 288
= 936 cm
2 Answer(s): (a) (2
n + 6) cm; b) 936 cm
2