5 Sided Shape Area Calculator

Find pentagon area from side, apothem, perimeter, or coordinate points quickly. Review formulas and examples. Download neat results for records, lessons, and projects today.

Calculator

Coordinate Points

Enter points in clockwise or counterclockwise order.

Formula Used

Regular Pentagon From Side

A = 1/4 × √(5(5 + 2√5)) × s²

Here, s is the length of one side.

Apothem And Perimeter Method

A = 1/2 × P × a

Here, P is perimeter and a is apothem.

Coordinate Method

A = 1/2 × |Σ(xᵢyᵢ₊₁ - yᵢxᵢ₊₁)|

This is the shoelace formula. Points must follow boundary order.

How To Use This Calculator

  1. Select the method that matches your known values.
  2. Choose the measurement unit.
  3. Enter side length, apothem and perimeter, or five points.
  4. Select decimal places for rounding.
  5. Press Calculate to view the result above the form.
  6. Use CSV or PDF buttons to save the result.

Example Data Table

Case Method Input Area
Example 1 Regular pentagon Side = 8 cm 110.1106 cm²
Example 2 Apothem and perimeter Apothem = 5.5055 cm, Perimeter = 40 cm 110.1100 cm²
Example 3 Coordinates (0,0), (4,0), (5,3), (2,5), (-1,3) 21.0000 units²

Understanding Five Sided Shape Area

A five sided shape is called a pentagon. Its area depends on its sides, angles, and point order. A regular pentagon has five equal sides. It also has equal angles. That makes its formula direct and dependable. An irregular pentagon needs a different method. The coordinate method is often best for that case.

Regular Pentagon Method

When one side is known, the calculator uses the standard regular pentagon formula. This formula builds area from side length only. It is useful for tiles, signs, badges, patterns, and geometry homework. You can also use apothem and perimeter. That method is simple. It treats the shape as five triangles meeting at the center. The apothem is the center to side distance. Perimeter is the total edge length. Area is one half of perimeter times apothem.

Coordinate Method

Many real five sided shapes are not regular. Their sides may be uneven. Their angles may change. For these cases, enter five ordered points. The tool applies the shoelace formula. This formula multiplies each point by the next point. It then subtracts the reverse products. The final absolute value gives area. Point order matters. Use clockwise or counterclockwise order around the boundary. Do not cross the edges unless the shape is meant to self overlap.

Why This Calculator Helps

This calculator keeps several methods in one form. You can choose units, rounding, and input type. The result shows area and useful supporting values. Regular mode also shows perimeter and apothem. Coordinate mode shows side lengths, perimeter, and centroid. These details help check the shape before using the area. They also make reports easier to explain.

Practical Accuracy Tips

Measure every length with the same unit. Use more decimals for precise design work. Round only at the end. For coordinates, confirm each point is placed in sequence. Sketch the pentagon before entering values. A quick sketch catches many mistakes. If the area seems too large, check unit choice. If it seems too small, check point order. For construction, add waste or margin separately. This tool gives geometric area. It does not include cutting loss, material overlap, or site adjustment. Save exports when you need clear evidence for later review or team sharing.

FAQs

What is a five sided shape called?

A five sided shape is called a pentagon. It can be regular or irregular. A regular pentagon has equal sides and equal angles.

Can this calculator find irregular pentagon area?

Yes. Choose the coordinate method. Enter all five points in order around the boundary. The calculator then uses the shoelace formula.

What is the regular pentagon area formula?

The formula is A = 1/4 × √(5(5 + 2√5)) × s². The variable s means one side length.

What is the apothem formula method?

The apothem method uses A = 1/2 × perimeter × apothem. It works well when the center to side distance is known.

Does point order matter for coordinates?

Yes. Enter points clockwise or counterclockwise. Mixed order can cross edges and create a wrong area.

Which unit should I choose?

Choose the unit used for your measurements. If lengths are in centimeters, area will be in square centimeters.

Can I download the results?

Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple report file.

Why is my coordinate area zero?

A zero area usually means the points are repeated, collinear, or entered in an invalid order. Check the shape sketch.


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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.