PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 15 cm, ST = 9 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 = 18.
(a)
Length WV
= 15 - 9
= 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
= 18 x 15
= 270 cm
2 Length UT
=
x + 6
= 18 + 6
= 24 cm
Area of Rectangle STUV
= 24 x 9
= 216 cm
2 Area of Triangle QRW
=
12 x 18 x 18
= 162 cm
2 Area of Triangle RSV
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 270 + 216 + 162 + 288
= 936 cm
2 Answer(s): (a) (2
x + 6) cm; b) 936 cm
2