PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 16 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 = 19.
(a)
Length XW
= 16 - 9
= 7 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 7) cm (Isosceles triangle)
Length QU
=
y +
y + 7
= (2
y + 7) cm
(b)
Area of Rectangle QRVX
= 19 x 16
= 304 cm
2 Length VU
=
y + 7
= 19 + 7
= 26 cm
Area of Rectangle TUVW
= 26 x 9
= 234 cm
2 Area of Triangle RSX
=
12 x 19 x 19
= 180.5 cm
2 Area of Triangle STW
=
12 x 26 x 26
= 338 cm
2 Total area of the figure
= 304 + 234 + 180.5 + 338
= 1056.5 cm
2 Answer(s): (a) (2
y + 7) cm; b) 1056.5 cm
2