PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 9 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 = 10.
(a)
Length HG
= 9 - 4
= 5 cm
Length CH =
j cm (Isosceles triangle)
Length GD
= Length CG
= (
j + 5) cm (Isosceles triangle)
Length AE
=
j +
j + 5
= (2
j + 5) cm
(b)
Area of Rectangle ABFH
= 10 x 9
= 90 cm
2 Length FE
=
j + 5
= 10 + 5
= 15 cm
Area of Rectangle DEFG
= 15 x 4
= 60 cm
2 Area of Triangle BCH
=
12 x 10 x 10
= 50 cm
2 Area of Triangle CDG
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 90 + 60 + 50 + 112.5
= 312.5 cm
2 Answer(s): (a) (2
j + 5) cm; b) 312.5 cm
2