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How to Calculate the Area of an Unequal Pentagon

You may be surprised to discover that the area of a pentagon, or five-sided polygon, can be difficult to calculate. Many of the pentagons presented to students are simple, or self-intersecting. But those in nature are often irregular with unequal sides. Calculating such pentagons requires creativity and previous knowledge of additional figures. Unequal polygons can be broken down into other shapes, or graphed on the Cartesian plane. Fortunately, there are a few tricks that make calculating complex pentagons an easy task.

Pencil
Paper
Calculator
Ruler

Instructions

- 1
  Draw all diagonals from the main vertex using a pencil and a ruler to divide the figure into triangles. Calculate the area of each triangle using the formula area = 1/2 *base*height. Add all the areas together to find the total sum of the irregular pentagon.
- 2
  Find the area of a regular pentagon if there is a portion of the overall figure missing. Subtract the area of the missing piece from the total area of the pentagon.
- 3
  Look for other shapes within the irregular pentagon, such as parallelograms and squares. Draw a line to separate the familiar shapes within the pentagon. Calculate the area of each figure, then add them together to find the total area of the unequal pentagon.

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