PSLEThe figure is made up of two rectangles, EFMK and KLHJ, and two right-angled isosceles triangles, FGM and HGL. FE = 13 cm, HJ = 8 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 = 19.
(a)
Length ML
= 13 - 8
= 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
= 19 x 13
= 247 cm
2 Length KJ
=
n + 5
= 19 + 5
= 24 cm
Area of Rectangle HJKL
= 24 x 8
= 192 cm
2 Area of Triangle FGM
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle GHL
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 247 + 192 + 180.5 + 288
= 907.5 cm
2 Answer(s): (a) (2
n + 5) cm; b) 907.5 cm
2