PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 12 cm, UV = 7 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 = 20.
(a)
Length YX
= 12 - 7
= 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
= 20 x 12
= 240 cm
2 Length WV
=
z + 5
= 20 + 5
= 25 cm
Area of Rectangle UVWX
= 25 x 7
= 175 cm
2 Area of Triangle STY
=
12 x 20 x 20
= 200 cm
2 Area of Triangle TUX
=
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
z + 5) cm; b) 927.5 cm
2