PSLEThe figure is made up of two rectangles, ABHF and FGDE, and two right-angled isosceles triangles, BCH and DCG. BA = 11 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 = 18.
(a)
Length HG
= 11 - 6
= 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
= 18 x 11
= 198 cm
2 Length FE
=
j + 5
= 18 + 5
= 23 cm
Area of Rectangle DEFG
= 23 x 6
= 138 cm
2 Area of Triangle BCH
=
12 x 18 x 18
= 162 cm
2 Area of Triangle CDG
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 198 + 138 + 162 + 264.5
= 762.5 cm
2 Answer(s): (a) (2
j + 5) cm; b) 762.5 cm
2