PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 18 cm, TU = 10 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 = 20.
(a)
Length XW
= 18 - 10
= 8 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 8) cm (Isosceles triangle)
Length QU
=
y +
y + 8
= (2
y + 8) cm
(b)
Area of Rectangle QRVX
= 20 x 18
= 360 cm
2 Length VU
=
y + 8
= 20 + 8
= 28 cm
Area of Rectangle TUVW
= 28 x 10
= 280 cm
2 Area of Triangle RSX
=
12 x 20 x 20
= 200 cm
2 Area of Triangle STW
=
12 x 28 x 28
= 392 cm
2 Total area of the figure
= 360 + 280 + 200 + 392
= 1232 cm
2 Answer(s): (a) (2
y + 8) cm; b) 1232 cm
2