Irregular Pentagon Area

The Area of an Irregular Pentagon calculator computes an area with five straight sides (a pentagon) 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  

Area of Irregular Pentagon (A): 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.
• Step 2 - From the point where Side E ends and Side A starts, measure the diagonal from (E,A) to (B,C). 
• Step 3 - Go back to the (E,A) corner and measure the diagonal to (C,D).     .

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

Pentagon Information

A pentagon is a polygon with five sides and five angles. It is a two-dimensional geometric shape formed by connecting five straight line segments (sides) in a closed loop. Each interior angle of a regular pentagon (where all sides and angles are equal) measures 108 degrees. The sum of the interior angles in any pentagon is 540 degrees.

Pentagons can come in various forms, and their sides and angles may have different lengths and measures. Regular pentagons are often encountered in geometry and design, and they have a symmetrical and balanced appearance. In practical terms, pentagons might be found in certain architectural elements, decorative patterns, and various other contexts.

Pentagon Calculators

• Pentagon Area: Regular pentagon area from side length.
• Irregular Pentagon Area: Area from sides and diagonals.
• Pentagon Side Length: Side length of regular pentagon from area.
• Pentagon Volume: Volume of regular pentagon column.
• Pentagon Planter: Soil volume and planting surface area of a pentagon shaped raised planter.
• Water in a Pentagon Pond: Water to fill a pentagon (regular) shaped pond at depth.
• Dodecahedron Surface Area: Surface area of regular dodecahedron based on side length.
• Dodecahedron Volume: Volume of regular dodecahedron based on side length.

In three dimensions, twelve (12) regular pentagons can be fused to form a dodecahedron.  A dodecahedron is a three-dimensional geometric shape characterized by having 12 flat faces, 20 vertices (corners), and 30 edges. Each face is a regular pentagon.  Dodecahedra can be found in various natural and man-made forms. In geometry, they are studied for their interesting properties and symmetrical characteristics. In certain games and puzzles, dodecahedra may also be used as components or shapes.