PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 12 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 = 18.
(a)
Length WV
= 12 - 7
= 5 cm
Length RW =
x cm (Isosceles triangle)
Length VS
= Length CG
= (
x + 5) cm (Isosceles triangle)
Length PT
=
x +
x + 5
= (2
x + 5) cm
(b)
Area of Rectangle PQUW
= 18 x 12
= 216 cm
2 Length UT
=
x + 5
= 18 + 5
= 23 cm
Area of Rectangle STUV
= 23 x 7
= 161 cm
2 Area of Triangle QRW
=
12 x 18 x 18
= 162 cm
2 Area of Triangle RSV
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 216 + 161 + 162 + 264.5
= 803.5 cm
2 Answer(s): (a) (2
x + 5) cm; b) 803.5 cm
2