PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 13 cm, UV = 8 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 = 16.
(a)
Length YX
= 13 - 8
= 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
= 16 x 13
= 208 cm
2 Length WV
=
z + 5
= 16 + 5
= 21 cm
Area of Rectangle UVWX
= 21 x 8
= 168 cm
2 Area of Triangle STY
=
12 x 16 x 16
= 128 cm
2 Area of Triangle TUX
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 208 + 168 + 128 + 220.5
= 724.5 cm
2 Answer(s): (a) (2
z + 5) cm; b) 724.5 cm
2