PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 12 cm, DE = 6 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 = 16.
(a)
Length HG
= 12 - 6
= 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
= 16 x 12
= 192 cm
2 Length FE
=
j + 6
= 16 + 6
= 22 cm
Area of Rectangle DEFG
= 22 x 6
= 132 cm
2 Area of Triangle BCH
=
12 x 16 x 16
= 128 cm
2 Area of Triangle CDG
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 192 + 132 + 128 + 242
= 694 cm
2 Answer(s): (a) (2
j + 6) cm; b) 694 cm
2