PSLEThe figure is made up of two rectangles, QRXV and VWTU, and two right-angled isosceles triangles, RSX and TSW. RQ = 13 cm, TU = 8 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
= 13 - 8
= 5 cm
Length SX =
y cm (Isosceles triangle)
Length WT
= Length CG
= (
y + 5) cm (Isosceles triangle)
Length QU
=
y +
y + 5
= (2
y + 5) cm
(b)
Area of Rectangle QRVX
= 16 x 13
= 208 cm
2 Length VU
=
y + 5
= 16 + 5
= 21 cm
Area of Rectangle TUVW
= 21 x 8
= 168 cm
2 Area of Triangle RSX
=
12 x 16 x 16
= 128 cm
2 Area of Triangle STW
=
12 x 21 x 21
= 220.5 cm
2 Total area of the figure
= 208 + 168 + 128 + 220.5
= 724.5 cm
2 Answer(s): (a) (2
y + 5) cm; b) 724.5 cm
2