PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 10 cm, TU = 6 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 = 13.
(a)
Length XW
= 10 - 6
= 4 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 4) cm (Isosceles triangle)
Length QU
=
y +
y + 4
= (2
y + 4) cm
(b)
Area of Rectangle QRVX
= 13 x 10
= 130 cm
2 Length VU
=
y + 4
= 13 + 4
= 17 cm
Area of Rectangle TUVW
= 17 x 6
= 102 cm
2 Area of Triangle RSX
=
12 x 13 x 13
= 84.5 cm
2 Area of Triangle STW
=
12 x 17 x 17
= 144.5 cm
2 Total area of the figure
= 130 + 102 + 84.5 + 144.5
= 461 cm
2 Answer(s): (a) (2
y + 4) cm; b) 461 cm
2