PSLEThe figure is made up of two rectangles, NPVT and TURS, and two right-angled isosceles triangles, PQV and RQU. PN = 9 cm, RS = 4 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 = 16.
(a)
Length VU
= 9 - 4
= 5 cm
Length QV =
w cm (Isosceles triangle)
Length UR
= Length CG
= (
w + 5) cm (Isosceles triangle)
Length NS
=
w +
w + 5
= (2
w + 5) cm
(b)
Area of Rectangle NPTV
= 16 x 9
= 144 cm
2 Length TS
=
w + 5
= 16 + 5
= 21 cm
Area of Rectangle RSTU
= 21 x 4
= 84 cm
2 Area of Triangle PQV
=
12 x 16 x 16
= 128 cm
2 Area of Triangle QRU
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 144 + 84 + 128 + 220.5
= 576.5 cm
2 Answer(s): (a) (2
w + 5) cm; b) 576.5 cm
2