PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 10 cm, UV = 6 cm and SY =
z cm. RWV and TYXW are straight lines.
- Find the length of RV in terms of z. Give your answer in the simplest form.
- Find the total area of the figure when z = 14.
(a)
Length YX
= 10 - 6
= 4 cm
Length TY =
z cm (Isosceles triangle)
Length XU
= Length CG
= (
z + 4) cm (Isosceles triangle)
Length RV
=
z +
z + 4
= (2
z + 4) cm
(b)
Area of Rectangle RSWY
= 14 x 10
= 140 cm
2 Length WV
=
z + 4
= 14 + 4
= 18 cm
Area of Rectangle UVWX
= 18 x 6
= 108 cm
2 Area of Triangle STY
=
12 x 14 x 14
= 98 cm
2 Area of Triangle TUX
=
12 x 18 x 18
= 162 cm
2 Total area of the figure
= 140 + 108 + 98 + 162
= 508 cm
2 Answer(s): (a) (2
z + 4) cm; b) 508 cm
2