PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 13 cm, ST = 8 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
= 13 - 8
= 5 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 5) cm (Isosceles triangle)
Length PT
=
x +
x + 5
= (2
x + 5) cm
(b)
Area of Rectangle PQUW
= 17 x 13
= 221 cm
2 Length UT
=
x + 5
= 17 + 5
= 22 cm
Area of Rectangle STUV
= 22 x 8
= 176 cm
2 Area of Triangle QRW
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle RSV
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 221 + 176 + 144.5 + 242
= 783.5 cm
2 Answer(s): (a) (2
x + 5) cm; b) 783.5 cm
2