PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 14 cm, DE = 9 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 = 20.
(a)
Length HG
= 14 - 9
= 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
= 20 x 14
= 280 cm
2 Length FE
=
j + 5
= 20 + 5
= 25 cm
Area of Rectangle DEFG
= 25 x 9
= 225 cm
2 Area of Triangle BCH
=
12 x 20 x 20
= 200 cm
2 Area of Triangle CDG
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 280 + 225 + 200 + 312.5
= 1017.5 cm
2 Answer(s): (a) (2
j + 5) cm; b) 1017.5 cm
2