PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 13 cm, DE = 7 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 = 15.
(a)
Length HG
= 13 - 7
= 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
= 15 x 13
= 195 cm
2 Length FE
=
j + 6
= 15 + 6
= 21 cm
Area of Rectangle DEFG
= 21 x 7
= 147 cm
2 Area of Triangle BCH
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle CDG
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 195 + 147 + 112.5 + 220.5
= 675 cm
2 Answer(s): (a) (2
j + 6) cm; b) 675 cm
2