PSLEThe figure is made up of two rectangles, NPVT and TURS, and two right-angled isosceles triangles, PQV and RQU. PN = 12 cm, RS = 7 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 = 20.
(a)
Length VU
= 12 - 7
= 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
= 20 x 12
= 240 cm
2 Length TS
=
w + 5
= 20 + 5
= 25 cm
Area of Rectangle RSTU
= 25 x 7
= 175 cm
2 Area of Triangle PQV
=
12 x 20 x 20
= 200 cm
2 Area of Triangle QRU
=
12 x 25 x 25
= 312.5 cm
2 Total area of the figure
= 240 + 175 + 200 + 312.5
= 927.5 cm
2 Answer(s): (a) (2
w + 5) cm; b) 927.5 cm
2