PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 7 cm, DE = 4 cm and BH =
j cm. AFE and CHGF are straight lines.
- Find the length of AE in terms of j. Give your answer in the simplest form.
- Find the total area of the figure when j = 11.
(a)
Length HG
= 7 - 4
= 3 cm
Length CH =
j cm (Isosceles triangle)
Length GD
= Length CG
= (
j + 3) cm (Isosceles triangle)
Length AE
=
j +
j + 3
= (2
j + 3) cm
(b)
Area of Rectangle ABFH
= 11 x 7
= 77 cm
2 Length FE
=
j + 3
= 11 + 3
= 14 cm
Area of Rectangle DEFG
= 14 x 4
= 56 cm
2 Area of Triangle BCH
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle CDG
=
12 x 14 x 14
= 98 cm
2 Total area of the figure
= 77 + 56 + 60.5 + 98
= 291.5 cm
2 Answer(s): (a) (2
j + 3) cm; b) 291.5 cm
2