PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 16 cm, ST = 9 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 = 17.
(a)
Length WV
= 16 - 9
= 7 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 7) cm (Isosceles triangle)
Length PT
=
x +
x + 7
= (2
x + 7) cm
(b)
Area of Rectangle PQUW
= 17 x 16
= 272 cm
2 Length UT
=
x + 7
= 17 + 7
= 24 cm
Area of Rectangle STUV
= 24 x 9
= 216 cm
2 Area of Triangle QRW
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle RSV
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 272 + 216 + 144.5 + 288
= 920.5 cm
2 Answer(s): (a) (2
x + 7) cm; b) 920.5 cm
2