PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 8 cm, TU = 5 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
= 8 - 5
= 3 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 3) cm (Isosceles triangle)
Length QU
=
y +
y + 3
= (2
y + 3) cm
(b)
Area of Rectangle QRVX
= 20 x 8
= 160 cm
2 Length VU
=
y + 3
= 20 + 3
= 23 cm
Area of Rectangle TUVW
= 23 x 5
= 115 cm
2 Area of Triangle RSX
=
12 x 20 x 20
= 200 cm
2 Area of Triangle STW
=
12 x 23 x 23
= 264.5 cm
2 Total area of the figure
= 160 + 115 + 200 + 264.5
= 739.5 cm
2 Answer(s): (a) (2
y + 3) cm; b) 739.5 cm
2