PSLEThe figure is made up of two rectangles, RSYW and WXUV, and two right-angled isosceles triangles, STY and UTX. SR = 15 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 = 17.
(a)
Length YX
= 15 - 8
= 7 cm
Length TY =
z cm (Isosceles triangle)
Length XU
= Length CG
= (
z + 7) cm (Isosceles triangle)
Length RV
=
z +
z + 7
= (2
z + 7) cm
(b)
Area of Rectangle RSWY
= 17 x 15
= 255 cm
2 Length WV
=
z + 7
= 17 + 7
= 24 cm
Area of Rectangle UVWX
= 24 x 8
= 192 cm
2 Area of Triangle STY
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle TUX
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 255 + 192 + 144.5 + 288
= 879.5 cm
2 Answer(s): (a) (2
z + 7) cm; b) 879.5 cm
2