PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 16 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 = 17.
(a)
Length XW
= 16 - 10
= 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
= 17 x 16
= 272 cm
2 Length VU
=
y + 6
= 17 + 6
= 23 cm
Area of Rectangle TUVW
= 23 x 10
= 230 cm
2 Area of Triangle RSX
=
12 x 17 x 17
= 144.5 cm
2 Area of Triangle STW
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 272 + 230 + 144.5 + 264.5
= 911 cm
2 Answer(s): (a) (2
y + 6) cm; b) 911 cm
2