PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 12 cm, ST = 6 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 = 14.
(a)
Length WV
= 12 - 6
= 6 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 6) cm (Isosceles triangle)
Length PT
=
x +
x + 6
= (2
x + 6) cm
(b)
Area of Rectangle PQUW
= 14 x 12
= 168 cm
2 Length UT
=
x + 6
= 14 + 6
= 20 cm
Area of Rectangle STUV
= 20 x 6
= 120 cm
2 Area of Triangle QRW
=
12 x 14 x 14
= 98 cm
2 Area of Triangle RSV
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 168 + 120 + 98 + 200
= 586 cm
2 Answer(s): (a) (2
x + 6) cm; b) 586 cm
2