PSLEThe figure is made up of two rectangles, BCJG and GHEF, and two right-angled isosceles triangles, CDJ and EDH. CB = 16 cm, EF = 9 cm and CJ =
k cm. BGF and DJHG are straight lines.
- Find the length of BF in terms of k. Give your answer in the simplest form.
- Find the total area of the figure when k = 18.
(a)
Length JH
= 16 - 9
= 7 cm
Length DJ =
k cm (Isosceles triangle)
Length HE
= Length CG
= (
k + 7) cm (Isosceles triangle)
Length BF
=
k +
k + 7
= (2
k + 7) cm
(b)
Area of Rectangle BCGJ
= 18 x 16
= 288 cm
2 Length GF
=
k + 7
= 18 + 7
= 25 cm
Area of Rectangle EFGH
= 25 x 9
= 225 cm
2 Area of Triangle CDJ
=
12 x 18 x 18
= 162 cm
2 Area of Triangle DEH
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 288 + 225 + 162 + 312.5
= 987.5 cm
2 Answer(s): (a) (2
k + 7) cm; b) 987.5 cm
2