PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 11 cm, ST = 7 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 = 15.
(a)
Length WV
= 11 - 7
= 4 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 4) cm (Isosceles triangle)
Length PT
=
x +
x + 4
= (2
x + 4) cm
(b)
Area of Rectangle PQUW
= 15 x 11
= 165 cm
2 Length UT
=
x + 4
= 15 + 4
= 19 cm
Area of Rectangle STUV
= 19 x 7
= 133 cm
2 Area of Triangle QRW
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle RSV
=
12 x 19 x 19
= 180.5 cm
2 Total area of the figure
= 165 + 133 + 112.5 + 180.5
= 591 cm
2 Answer(s): (a) (2
x + 4) cm; b) 591 cm
2