PSLEThe figure is made up of two rectangles, BCJG and GHEF, and two right-angled isosceles triangles, CDJ and EDH. CB = 7 cm, EF = 4 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 = 20.
(a)
Length JH
= 7 - 4
= 3 cm
Length DJ =
k cm (Isosceles triangle)
Length HE
= Length CG
= (
k + 3) cm (Isosceles triangle)
Length BF
=
k +
k + 3
= (2
k + 3) cm
(b)
Area of Rectangle BCGJ
= 20 x 7
= 140 cm
2 Length GF
=
k + 3
= 20 + 3
= 23 cm
Area of Rectangle EFGH
= 23 x 4
= 92 cm
2 Area of Triangle CDJ
=
12 x 20 x 20
= 200 cm
2 Area of Triangle DEH
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 140 + 92 + 200 + 264.5
= 696.5 cm
2 Answer(s): (a) (2
k + 3) cm; b) 696.5 cm
2