PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 9 cm, TU = 5 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 = 16.
(a)
Length XW
= 9 - 5
= 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
= 16 x 9
= 144 cm
2 Length VU
=
y + 4
= 16 + 4
= 20 cm
Area of Rectangle TUVW
= 20 x 5
= 100 cm
2 Area of Triangle RSX
=
12 x 16 x 16
= 128 cm
2 Area of Triangle STW
=
12 x 20 x 20
= 200 cm
2 Total area of the figure
= 144 + 100 + 128 + 200
= 572 cm
2 Answer(s): (a) (2
y + 4) cm; b) 572 cm
2