How to calculate the area & perimeter of the oval ground? /Calculating the area & perimeter of oval ( ellipse ) shaped land.

Let us calculate the area & perimeter of the oval-shaped playground as shown below.

Given data:

   Major axis = 155m.

   Minor axis =125m.

Calculation:

1. Area calculation

The given oval-shaped ground is an ellipse

So, the area is calculated by the formula

A  = [π × {( major axis + minor axis ) ÷ 2}]

     = [ 3.142 × {( 155m + 125m ) ÷ 2}]

     =  [ 3.142 × {280 ÷ 2}]

     =[ 3.142 × 140]

     = 439.88 sq m.

Area of the oval ground = 439.88 sq m.

2. Perimeter calculation:

The perimeter of the oval ground can be calculated by using different types of formulas. None of the formulas gives accurate results for the perimeter.

Let us calculate the perimeter of the ground by using 2 different formulas.

The 2nd formula, also known as the Ramanujan formula gives nearer to accurate results.

a. The perimeter of the ground (formula -1)

    P  ≈ [2π × √ {( a2 + b2) ÷ 2}]

Where a = semi-major axis of the ground.

            b = semi-minor axis of the ground

For your understanding, I have redrawn the oval ground with a, b, & P as shown below.

    Here, a = [major-axis ÷ 2 ]

                 = [155m ÷ 2]

                 =77.5m.

              b = [minor-axis ÷ 2 ]

                 = [125m ÷ 2]

                 = 62.5m.

Putting the values in the above formula,

     P ≈ [(2 × 3.142) × √ { ( 77.52 + 62.52)÷ 2}]

     P ≈ [6.284 × √ {(6006.25 + 3906.25)÷ 2}]

     P ≈ [6.284 × √ {9912.5÷ 2} ]

     P ≈ [6.284 × √ 4956.25 ]

     P ≈ [6.284 × 70.40 ]

    P ≈ 442.39m.

b. Nearer to accurate calculation (formula -2 )

  Ramanujan formula to calculate the perimeter

    P = [π × (a +b ) × { 3-  √ (4 -h )}]

Where, h= [ (a-b)2 ÷ (a+b)2 ] 

   First, we will calculate the value of h.

       h = [ (77.5-62.5)2 ÷ (77.5+62.5)2 ] 

       h = [ (15)2 ÷ (140)2 ] 

          = [ 225  ÷ 19600 ] 

          = 0.01148

   Perimeter = [π × (a +b ) × { 3-  √ (4 -h )}]

    By putting the values of a, b, & h

     P = [3.142 × (77.5 +62.5 ) × { 3 - √ (4 - 0.01148 )}]

         = [3.142 × (140 ) × { 3 - √ (3.988 )}]

         = [3.142 × 140  × { 3 - 1.997}]

         =  [3.142 × 140  × 1.003]

          = 441.20 m.

The perimeter of the oval ground by formula -1 = 442.39m.

The perimeter of the oval ground by formula -2 = 441.20m.

To go through the articles on Estimation & calculation in civil engineering, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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