PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 11 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 = 15.
(a)
Length YX
= 11 - 6
= 5 cm
Length TY =
z cm (Isosceles triangle)
Length XU
= Length CG
= (
z + 5) cm (Isosceles triangle)
Length RV
=
z +
z + 5
= (2
z + 5) cm
(b)
Area of Rectangle RSWY
= 15 x 11
= 165 cm
2 Length WV
=
z + 5
= 15 + 5
= 20 cm
Area of Rectangle UVWX
= 20 x 6
= 120 cm
2 Area of Triangle STY
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle TUX
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 165 + 120 + 112.5 + 200
= 597.5 cm
2 Answer(s): (a) (2
z + 5) cm; b) 597.5 cm
2