PSLEThe figure is made up of two rectangles, NPVT and TURS, and two right-angled isosceles triangles, PQV and RQU. PN = 8 cm, RS = 5 cm and PV =
w cm. NTS and QVUT are straight lines.
- Find the length of NS in terms of w. Give your answer in the simplest form.
- Find the total area of the figure when w = 17.
(a)
Length VU
= 8 - 5
= 3 cm
Length QV =
w cm (Isosceles triangle)
Length UR
= Length CG
= (
w + 3) cm (Isosceles triangle)
Length NS
=
w +
w + 3
= (2
w + 3) cm
(b)
Area of Rectangle NPTV
= 17 x 8
= 136 cm
2 Length TS
=
w + 3
= 17 + 3
= 20 cm
Area of Rectangle RSTU
= 20 x 5
= 100 cm
2 Area of Triangle PQV
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle QRU
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 136 + 100 + 144.5 + 200
= 580.5 cm
2 Answer(s): (a) (2
w + 3) cm; b) 580.5 cm
2