PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 9 cm, ST = 5 cm and QW =
x cm. PUT and RWVU are straight lines.
- Find the length of PT in terms of x. Give your answer in the simplest form.
- Find the total area of the figure when x = 20.
(a)
Length WV
= 9 - 5
= 4 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 4) cm (Isosceles triangle)
Length PT
=
x +
x + 4
= (2
x + 4) cm
(b)
Area of Rectangle PQUW
= 20 x 9
= 180 cm
2 Length UT
=
x + 4
= 20 + 4
= 24 cm
Area of Rectangle STUV
= 24 x 5
= 120 cm
2 Area of Triangle QRW
=
12 x 20 x 20
= 200 cm
2 Area of Triangle RSV
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 180 + 120 + 200 + 288
= 788 cm
2 Answer(s): (a) (2
x + 4) cm; b) 788 cm
2