PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 7 cm, TU = 4 cm and RX =
y cm. QVU and SXWV are straight lines.
- Find the length of QU in terms of y. Give your answer in the simplest form.
- Find the total area of the figure when y = 11.
(a)
Length XW
= 7 - 4
= 3 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 3) cm (Isosceles triangle)
Length QU
=
y +
y + 3
= (2
y + 3) cm
(b)
Area of Rectangle QRVX
= 11 x 7
= 77 cm
2 Length VU
=
y + 3
= 11 + 3
= 14 cm
Area of Rectangle TUVW
= 14 x 4
= 56 cm
2 Area of Triangle RSX
=
12 x 11 x 11
= 60.5 cm
2 Area of Triangle STW
=
12 x 14 x 14
= 98 cm
2 Total area of the figure
= 77 + 56 + 60.5 + 98
= 291.5 cm
2 Answer(s): (a) (2
y + 3) cm; b) 291.5 cm
2