PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 15 cm, TU = 9 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
= 15 - 9
= 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
= 16 x 15
= 240 cm
2 Length VU
=
y + 6
= 16 + 6
= 22 cm
Area of Rectangle TUVW
= 22 x 9
= 198 cm
2 Area of Triangle RSX
=
12 x 16 x 16
= 128 cm
2 Area of Triangle STW
=
12 x 22 x 22
= 242 cm
2 Total area of the figure
= 240 + 198 + 128 + 242
= 808 cm
2 Answer(s): (a) (2
y + 6) cm; b) 808 cm
2