Question

In given figure depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segments is $60m$ and they are each $106m$ long. If the track is $10m$ wide, find:
(i) The distance around the track along its inner edge
(ii) The area of the track

Answer 1

The distance around the track along its inner edge
$=EF+HG$ $+$ circumference of semicircle with diameter $EH+$circumference of semicircle with diameter $FG$
circumference of semicircle with diameter $EH$ $+$ Circumference of semicircle with diameter $FG$
$=2\times \pi \times 30=60\pi m$
$\therefore$ The distance around the track along its inner edge
$=60\pi +106+106$
$=\frac{2804}{7}m$
$\therefore$ Area of track $=$ Area of rectangle $ABFE$ $+$ Area of rectangle $HGCD$ $+$ (Area of semicircle with diameter $AD$ $-$ Area of semicircle with diameter $EH$) $+$ (Area of semicircle with diameter $BC$ $-$ Area of semicircle with diameter $FG$)
$=(106\times 10)$+$(106\times 10)$+$(\frac{\pi }{2}\times 40\times 40-\frac{\pi }{2}\times 30\times 30)$+$(\frac{\pi }{2}\times 40\times 40-\frac{\pi }{2}\times 30\times 30)$
$=2120+2200=4320m^2$