PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 12 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 = 15.
(a)
Length XW
= 12 - 6
= 6 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 6) cm (Isosceles triangle)
Length QU
=
y +
y + 6
= (2
y + 6) cm
(b)
Area of Rectangle QRVX
= 15 x 12
= 180 cm
2 Length VU
=
y + 6
= 15 + 6
= 21 cm
Area of Rectangle TUVW
= 21 x 6
= 126 cm
2 Area of Triangle RSX
=
12 x 15 x 15
= 112.5 cm
2 Area of Triangle STW
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 180 + 126 + 112.5 + 220.5
= 639 cm
2 Answer(s): (a) (2
y + 6) cm; b) 639 cm
2