PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 7 cm, UV = 4 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 = 18.
(a)
Length YX
= 7 - 4
= 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
= 18 x 7
= 126 cm
2 Length WV
=
z + 3
= 18 + 3
= 21 cm
Area of Rectangle UVWX
= 21 x 4
= 84 cm
2 Area of Triangle STY
=
12 x 18 x 18
= 162 cm
2 Area of Triangle TUX
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 126 + 84 + 162 + 220.5
= 592.5 cm
2 Answer(s): (a) (2
z + 3) cm; b) 592.5 cm
2