Question

Find the the perimeter of the figure given correct to one decimal place.

• A. $56.0m$
• B. $56.6m$
• C. $57.7m$
• D. $57.9m$

Answer 1

Answer: (B)

$56.6m$

The perimeter of the given figure $=AB+CD+EF+GH+4\times$ ( Perimeter of a quadrant of the circle ) $....\left(1\right)$

Now, $AB=EF=20m-(2m+2m)=16m$

Similarly, $CD=GH=10m-(2m+2m)=6m$

Now, the perimeter of the quadrant having radius $2m$

$=\frac{2\pi r}{4}$

$=\frac{\pi r}{2}$

$=\frac{\pi \times 2}{2}$

$=\pi$

So, the perimeter of the $4$ quadrants having radius $2m=4\pi$

Put all the respective values in $\left(1\right)$, we get

Perimeter of the given figure $=16m+6m+16m+6m+4$ $\pi$

$=44m+(4\times 3.14)$

$=44+12.56$

$=56.56m\sim 56.6m$

Hence, the perimeter of the given figure correct to one decimal place is 56.6 m.