PSLEThe figure is made up of two rectangles, NPVT and TURS, and two right-angled isosceles triangles, PQV and RQU. PN = 11 cm, RS = 6 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 = 19.
(a)
Length VU
= 11 - 6
= 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
= 19 x 11
= 209 cm
2 Length TS
=
w + 5
= 19 + 5
= 24 cm
Area of Rectangle RSTU
= 24 x 6
= 144 cm
2 Area of Triangle PQV
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle QRU
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 209 + 144 + 180.5 + 288
= 821.5 cm
2 Answer(s): (a) (2
w + 5) cm; b) 821.5 cm
2