PSLEThe figure is made up of two rectangles, BCJG and GHEF, and two right-angled isosceles triangles, CDJ and EDH. CB = 15 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
= 15 - 9
= 6 cm
Length DJ =
k cm (Isosceles triangle)
Length HE
= Length CG
= (
k + 6) cm (Isosceles triangle)
Length BF
=
k +
k + 6
= (2
k + 6) cm
(b)
Area of Rectangle BCGJ
= 18 x 15
= 270 cm
2 Length GF
=
k + 6
= 18 + 6
= 24 cm
Area of Rectangle EFGH
= 24 x 9
= 216 cm
2 Area of Triangle CDJ
=
12 x 18 x 18
= 162 cm
2 Area of Triangle DEH
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 270 + 216 + 162 + 288
= 936 cm
2 Answer(s): (a) (2
k + 6) cm; b) 936 cm
2