PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 15 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
= 15 - 9
= 6 cm
Length CH =
j cm (Isosceles triangle)
Length GD
= Length CG
= (
j + 6) cm (Isosceles triangle)
Length AE
=
j +
j + 6
= (2
j + 6) cm
(b)
Area of Rectangle ABFH
= 20 x 15
= 300 cm
2 Length FE
=
j + 6
= 20 + 6
= 26 cm
Area of Rectangle DEFG
= 26 x 9
= 234 cm
2 Area of Triangle BCH
=
12 x 20 x 20
= 200 cm
2 Area of Triangle CDG
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 300 + 234 + 200 + 338
= 1072 cm
2 Answer(s): (a) (2
j + 6) cm; b) 1072 cm
2