PSLEThe figure is made up of two rectangles, PQWU and UVST, and two right-angled isosceles triangles, QRW and SRV. QP = 16 cm, ST = 10 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 = 19.
(a)
Length WV
= 16 - 10
= 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
= 19 x 16
= 304 cm
2 Length UT
=
x + 6
= 19 + 6
= 25 cm
Area of Rectangle STUV
= 25 x 10
= 250 cm
2 Area of Triangle QRW
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle RSV
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 304 + 250 + 180.5 + 312.5
= 1047 cm
2 Answer(s): (a) (2
x + 6) cm; b) 1047 cm
2