PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 10 cm, ST = 5 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 = 16.
(a)
Length WV
= 10 - 5
= 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
= 16 x 10
= 160 cm
2 Length UT
=
x + 5
= 16 + 5
= 21 cm
Area of Rectangle STUV
= 21 x 5
= 105 cm
2 Area of Triangle QRW
=
12 x 16 x 16
= 128 cm
2 Area of Triangle RSV
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 160 + 105 + 128 + 220.5
= 613.5 cm
2 Answer(s): (a) (2
x + 5) cm; b) 613.5 cm
2