Pentagon Area Calculator
How to use this Pentagon Area Calculator 🤔
- Enter ✎ value for length of side (s).
- As soon as you enter the required input value(s), the Pentagon Area is calculated immediately, and displaed in the output section (present under input section).
Calculation
Once you enter the input values in the calculator, the output parameters are calculated.
Examples
The following examples cover how to calcualte the Area when length of side is given.
1. What is the Area of Pentagon whose length of side is 20 units?
Answer
Given:
- length of side, s = 20 units
The formula to find the Area of a Pentagon is:
A = \( \frac{ \sqrt{5(5 + 2\sqrt{5})} }{4} s ^2 \)
Substitute given values in the above formula.
A = \( \frac{ \sqrt{5(5 + 2\sqrt{5})} }{4} \times20^2 \)
A = 688.19 square units
∴ Area, A = 688.19 square units
2. What is the Area of Pentagon whose length of side is 1 units?
Answer
Given:
- length of side, s = 1 units
The formula to find the Area of a Pentagon is:
A = \( \frac{ \sqrt{5(5 + 2\sqrt{5})} }{4} s ^2 \)
Substitute given values in the above formula.
A = \( \frac{ \sqrt{5(5 + 2\sqrt{5})} }{4} \times1^2 \)
A = 1.72 square units
∴ Area, A = 1.72 square units
{
"topic": "pentagon-area",
"img": {
"width": 245,
"height": 273
},
"input_types": [
"float"
],
"input_labels": [
"s"
],
"input_values": [
"8"
],
"input_units": [
"units"
],
"input_descriptions": [
"length of side"
],
"examples": [
{
"s": 20
},
{
"s": 1
}
],
"type": "Calculate",
"title": "Pentagon Area",
"category": "Geometry",
"shape": "Pentagon",
"formula_mathjax": "\\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} s ^2 \\)",
"formula_mathjax_sub": "\\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} \\times s ^2 \\)",
"formula": "( Math.sqrt(5*(5+2*Math.sqrt(5))) * s * s / 4 )",
"op_label": "Area",
"output_unit": "square units",
"description": "The Pentagon Area calculator calculates the area of a pentagon shape by taking the length of its side as input.",
"explanation": "The area of a regular pentagon is a measure of the space enclosed by its five equal sides. To calculate the area of a pentagon using length of the side, use the given formula for pentagon area, and compute the result.",
"examples_data": "<h2>Examples</h2><p>The following examples cover how to calcualte the Area when length of side is given.</p><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> What is the Area of Pentagon whose length of side is 20 units?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>length of side, s = 20 units</ul><p>The formula to find the Area of a Pentagon is:</p><p class=\"tabspace\">A = \\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} s ^2 \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">A = \\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} \\times20^2 \\)</p><p class=\"tabspace\">A = 688.19 square units</p><p class=\"tabspace answer\">∴ Area, A = 688.19 square units</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> What is the Area of Pentagon whose length of side is 1 units?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>length of side, s = 1 units</ul><p>The formula to find the Area of a Pentagon is:</p><p class=\"tabspace\">A = \\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} s ^2 \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">A = \\( \\frac{ \\sqrt{5(5 + 2\\sqrt{5})} }{4} \\times1^2 \\)</p><p class=\"tabspace\">A = 1.72 square units</p><p class=\"tabspace answer\">∴ Area, A = 1.72 square units</p></div>",
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