PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 8 cm, DE = 5 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 = 10.
(a)
Length HG
= 8 - 5
= 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
= 10 x 8
= 80 cm
2 Length FE
=
j + 3
= 10 + 3
= 13 cm
Area of Rectangle DEFG
= 13 x 5
= 65 cm
2 Area of Triangle BCH
=
12 x 10 x 10
= 50 cm
2 Area of Triangle CDG
=
12 x 13 x 13
= 84.5 cm
2 Total area of the figure
= 80 + 65 + 50 + 84.5
= 279.5 cm
2 Answer(s): (a) (2
j + 3) cm; b) 279.5 cm
2