Five Sided Land Size

The Five Sided Land Size calculator computes the acres, square feet and perimeter of land with five straight sides given the length of the five sides and two diagonals (see image).

INSTRUCTIONS:  Choose units and enter the following:

• (A) Length of Side A
• (B) Length of Side B
• (C) Length of Side C
• (D) Length of Side D
• (E) Length of Side E
• (F) Length of Diagonal F
• (G) Length of Diagonal G  

Total Area of a 5 Sided Field (TA): The area is returned in acres, square feet, square meters and hectares

The Math / Science

To compute the area of a polygon, one must reduce the measurements down to non-overlapping triangles.  This is why the diagonals are needed. 

WHAT DIAGONALS TO CHOOSE

Since we are defining triangles, it's important to get the order correct.  Pick any corner, and consider that corner as where side A begins, and as the point to measure your two diagonals.  

• Step 1 - Pick any corner, and measure sides A, B, C, D and E. That first corner is the ORIGEN. 
• Step 2 - From the ORIGEN, measure the diagonal to corner where Side B meets Side C (G Diagonal). 
• Step 3 - Go back to the ORIGEN and measure the diagonal to where Side C meets Side D (F Diagonal).

Enter those lengths into this calculator and you will have an accurate measure of the area (TA).

The Total Area of a 5 Sided field has to be calculated based on three triangles (A,B,G), (G,F,C) and (E,F,D).  The area of the 5 sided field is the sum of those three triangles.

Once the triangles have been measured, on can use the formula for the area of a triangle based on the length of the three sides, which is:

        `A = sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c))`

where:

• A is the area of the triangle
• a is the length of one side
• b is the length of one side
• c is the length of one side

Land Size Calculators

• Three Sided Land Size: Computes the square feet, acres and perimeter in land with three straight sides.
• Four Sided Land Size (squared): Computes the area in square feet and acres and perimeter in feet of rectangle land with roughly squared corners based on the length and width.  
• Four Sided Land Size (not squared): Computes the area and perimeter of four sided land based on side lengths and a length of a diagonal.
• Five Sided Land Size: Computes the area and perimeter of a five sided land based on side lengths and the lengths of two diagonals.
• Circular Land Size: Computes the area of land in roughly circular shape based on the width (diameter). 
• Simi-Circular Land Size: Computes the area of land in roughly semi-circular shape based on the width (diameter). 
• Oval Shaped Land Size: Computes the area of land in roughly an oval (ellipse) shape based on the length and width.
• Human Paces to Feet and Meters: Estimates a length (feet, yards and meters) based on the number of paces a person takes to walk it and the approximate length of stride.

Walking Measurements

For large areas (lawns, gardens or fields), it may be hard to measure longer lengths, because you have no measuring device to make the long measurements (electronic device or long measuring tape or twine).  In this case, an estimate can be achieved by using paces (your steps).  

To estimate a length with paces, you first have to make a reasonable estimate of a regular pace while in stride.  To do this, put a mark on the ground, and step back several paces.  Start walking to the mark, and start counting some number of paces past the mark (e.g. 10).  A that point, stop and measure the length.  For example a man of six feet tall with a normal stride walked 14 paces in 40 feet.  That gave him a feet per pace of 2.857 feet per pace.  To compute the Feet per Pace, CLICK HERE.   You can then walk off the measurements, using a steady pace, and convert the Paces to Feet by CLICKING HERE.  It's a rough estimation method, but not without it's uses.

Often it is required to put land pieces together to compute to total area of land.  The land shown can be accurately computed by individual triangles. The area of 5 sided land function requires the diagonals that create three triangles that are summed to compute the area in a 5 sided piece of land.