PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 8 cm, UV = 5 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 = 19.
(a)
Length YX
= 8 - 5
= 3 cm
Length TY =
z cm (Isosceles triangle)
Length XU
= Length CG
= (
z + 3) cm (Isosceles triangle)
Length RV
=
z +
z + 3
= (2
z + 3) cm
(b)
Area of Rectangle RSWY
= 19 x 8
= 152 cm
2 Length WV
=
z + 3
= 19 + 3
= 22 cm
Area of Rectangle UVWX
= 22 x 5
= 110 cm
2 Area of Triangle STY
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle TUX
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 152 + 110 + 180.5 + 242
= 684.5 cm
2 Answer(s): (a) (2
z + 3) cm; b) 684.5 cm
2