PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 7 cm, ST = 4 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
= 7 - 4
= 3 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 3) cm (Isosceles triangle)
Length PT
=
x +
x + 3
= (2
x + 3) cm
(b)
Area of Rectangle PQUW
= 14 x 7
= 98 cm
2 Length UT
=
x + 3
= 14 + 3
= 17 cm
Area of Rectangle STUV
= 17 x 4
= 68 cm
2 Area of Triangle QRW
=
12 x 14 x 14
= 98 cm
2 Area of Triangle RSV
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 98 + 68 + 98 + 144.5
= 408.5 cm
2 Answer(s): (a) (2
x + 3) cm; b) 408.5 cm
2