Not so Simple

First we have to find perimeter of ellipse and there are number of formulas by which we can do so. Hence I have put "Approx" word. To find perimeter of ellipse we first have to find . = 0.15747 Simplifying the same we get, put a = 22 put b = 9.5 put h = 0.15747 Final answer of perimeter of ellipse will be 102.8575 We have two half ellipse hence its total perimeter will be 1/2 (102.8575 * 2 ellipse) = 102.8575. Now add remaining portion of the shape which is 35 + 35 + 2 + 2 = 74. And final perimeter of the shape will be 102.8575 + 74 = 176.8575.

First we have to find perimeter of ellipse and there are number of formulas by which we can do so. Hence I have put "Approx" word.

To find perimeter of ellipse we first have to find $h$ .

$h=\frac { { (a-b })^{ 2 } }{ { (a+b) }^{ 2 } }$

$h=\frac { { (22-9.5 })^{ 2 } }{ { (22+9.5) }^{ 2 } }$

= 0.15747

$p=\pi (a+b)\sum _{ n=0 }^{ \infty }{ \left( \overset { 0.5 }{ \underset { n }{ } } \right) } ^{ 2 }{ h }^{ n }$

Simplifying the same we get,

$p=\pi (a+b)\left( 1+\frac { 1 }{ 4 } h+\frac { 1 }{ 64 } { h }^{ 2 }+\frac { 1 }{ 256 } { h }^{ 3 }+.... \right)$

put a = 22

put b = 9.5

put h = 0.15747

Final answer of perimeter of ellipse will be 102.8575

We have two half ellipse hence its total perimeter will be 1/2 (102.8575 * 2 ellipse) = 102.8575.

Now add remaining portion of the shape which is 35 + 35 + 2 + 2 = 74.

And final perimeter of the shape will be 102.8575 + 74 = 176.8575.

May take a look at external source here .