PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 11 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 = 19.
(a)
Length XW
= 11 - 6
= 5 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 5) cm (Isosceles triangle)
Length QU
=
y +
y + 5
= (2
y + 5) cm
(b)
Area of Rectangle QRVX
= 19 x 11
= 209 cm
2 Length VU
=
y + 5
= 19 + 5
= 24 cm
Area of Rectangle TUVW
= 24 x 6
= 144 cm
2 Area of Triangle RSX
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle STW
=
12 x 24 x 24
= 288 cm
2 Total area of the figure
= 209 + 144 + 180.5 + 288
= 821.5 cm
2 Answer(s): (a) (2
y + 5) cm; b) 821.5 cm
2