PSLEThe figure is made up of two rectangles, NPVT and TURS, and two right-angled isosceles triangles, PQV and RQU. PN = 10 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 = 11.
(a)
Length VU
= 10 - 6
= 4 cm
Length QV =
w cm (Isosceles triangle)
Length UR
= Length CG
= (
w + 4) cm (Isosceles triangle)
Length NS
=
w +
w + 4
= (2
w + 4) cm
(b)
Area of Rectangle NPTV
= 11 x 10
= 110 cm
2 Length TS
=
w + 4
= 11 + 4
= 15 cm
Area of Rectangle RSTU
= 15 x 6
= 90 cm
2 Area of Triangle PQV
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle QRU
=
12 x 15 x 15
= 112.5 cm
2 Total area of the figure
= 110 + 90 + 60.5 + 112.5
= 373 cm
2 Answer(s): (a) (2
w + 4) cm; b) 373 cm
2