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Base Area of Pentagonal Pyramid Calculator

Formula

The formula to calculate the Base Area of a Pentagonal Pyramid given its edge length is:

$\text{Base Area} = \frac{1}{4} \cdot \sqrt{5 \cdot (5 + 2\sqrt{5})} \cdot \text{Edge Length}^2$

Definition

The Base Area of a Pentagonal Pyramid is the total amount of two-dimensional space occupied on the base surface of the pentagonal pyramid. The edge length of the base of the pentagonal pyramid is the length of the straight line connecting any two adjacent vertices of the base.

Example Calculation

Let's assume the following value:

Edge Length = 10 meters

Using the formula:

$\text{Base Area} = \frac{1}{4} \cdot \sqrt{5 \cdot (5 + 2\sqrt{5})} \cdot 10^2 \approx 172.0477 \, \text{square meters}$

The Base Area is approximately 172.0477 square meters.

Conversion Chart

Edge Length (meters)	Base Area (square meters)
8	110.110553637693883
9	139.358669447706319
10	172.047740058896693
11	208.177765471264991
12	247.748745684811240