PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 17 cm, ST = 10 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
= 17 - 10
= 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
= 20 x 17
= 340 cm
2 Length UT
=
x + 7
= 20 + 7
= 27 cm
Area of Rectangle STUV
= 27 x 10
= 270 cm
2 Area of Triangle QRW
=
12 x 20 x 20
= 200 cm
2 Area of Triangle RSV
=
12 x 27 x 27
= 364.5 cm
2 Total area of the figure
= 340 + 270 + 200 + 364.5
= 1174.5 cm
2 Answer(s): (a) (2
x + 7) cm; b) 1174.5 cm
2