The Formula for Finding the Area of a Polygon

Oct 13, 2025 by wbrum.org 132 views

Introduction

In mathematics, the area of a polygon is a fundamental concept that is used to calculate the amount of space inside a two-dimensional shape. Polygons are shapes with multiple sides, and they can be regular or irregular. In this article, we will discuss how to find the area of each polygon, using a specific example to illustrate the concept.

What is a Polygon?

A polygon is a two-dimensional shape with at least three sides and angles. It can be regular or irregular, and it can have any number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, and hexagons. In this article, we will focus on finding the area of a specific type of polygon, which is a quadrilateral.

The Formula for Finding the Area of a Polygon

The formula for finding the area of a polygon is:

Area = (base × height) / 2

This formula is used to calculate the area of a triangle, but it can also be used to calculate the area of a quadrilateral by breaking it down into two triangles.

Breaking Down a Quadrilateral into Two Triangles

To find the area of a quadrilateral, we can break it down into two triangles by drawing a diagonal from one vertex to the opposite vertex. This will create two triangles, each with a base and a height. We can then use the formula above to calculate the area of each triangle, and add them together to find the total area of the quadrilateral.

Example: Finding the Area of a Quadrilateral

Let's use the example given in the problem statement to find the area of a quadrilateral. The quadrilateral has the following side lengths:

2 ft
4 ft
10 ft
14 ft

We can break this quadrilateral down into two triangles by drawing a diagonal from one vertex to the opposite vertex. Let's call the two triangles Triangle A and Triangle B.

Triangle A

Triangle A has a base of 2 ft and a height of 4 ft. We can use the formula above to calculate the area of Triangle A:

Area = (base × height) / 2 = (2 × 4) / 2 = 4

Triangle B

Triangle B has a base of 10 ft and a height of 14 ft. We can use the formula above to calculate the area of Triangle B:

Area = (base × height) / 2 = (10 × 14) / 2 = 70

Finding the Total Area of the Quadrilateral

Now that we have found the area of each triangle, we can add them together to find the total area of the quadrilateral:

Total Area = Area of Triangle A + Area of Triangle B = 4 + 70 = 74

Therefore, the area of the quadrilateral is 74 square feet.

Conclusion

In this article, we discussed how to find the area of each polygon, using a specific example to illustrate the concept. We learned that the formula for finding the area of a polygon is (base × height) / 2, and that we can break down a quadrilateral into two triangles by drawing a diagonal from one vertex to the opposite vertex. We also learned how to calculate the area of each triangle and add them together to find the total area of the quadrilateral. With this knowledge, you can now find the area of any polygon, whether it is a triangle, quadrilateral, pentagon, or hexagon.

Frequently Asked Questions

What is the formula for finding the area of a polygon? The formula for finding the area of a polygon is (base × height) / 2.
How do I break down a quadrilateral into two triangles? To break down a quadrilateral into two triangles, draw a diagonal from one vertex to the opposite vertex.
How do I calculate the area of each triangle? To calculate the area of each triangle, use the formula (base × height) / 2.
How do I find the total area of the quadrilateral? To find the total area of the quadrilateral, add the area of each triangle together.

References

Math Open Reference. (n.d.). Polygon. Retrieved from https://www.mathopenref.com/polygon.html
Khan Academy. (n.d.). Area of a polygon. Retrieved from https://www.khanacademy.org/math/geometry/area-of-polygons/area-of-polygons/v/area-of-polygons

Glossary

Polygon: A two-dimensional shape with at least three sides and angles.
Quadrilateral: A polygon with four sides and angles.
Triangle: A polygon with three sides and angles.
Base: The length of the side of a polygon that is used to calculate its area.
Height: The length of the perpendicular line from the base of a polygon to its opposite vertex.
Area: The amount of space inside a two-dimensional shape.

Introduction

In our previous article, we discussed how to find the area of each polygon, using a specific example to illustrate the concept. However, we know that there are many more questions that you may have about finding the area of polygons. In this article, we will answer some of the most frequently asked questions about finding the area of polygons.

Q: What is the formula for finding the area of a polygon?

A: The formula for finding the area of a polygon is (base × height) / 2. This formula is used to calculate the area of a triangle, but it can also be used to calculate the area of a quadrilateral by breaking it down into two triangles.

Q: How do I break down a quadrilateral into two triangles?

A: To break down a quadrilateral into two triangles, draw a diagonal from one vertex to the opposite vertex. This will create two triangles, each with a base and a height. You can then use the formula above to calculate the area of each triangle, and add them together to find the total area of the quadrilateral.

Q: How do I calculate the area of each triangle?

A: To calculate the area of each triangle, use the formula (base × height) / 2. Make sure to use the correct base and height for each triangle, and then add the areas together to find the total area of the quadrilateral.

Q: What if I have a polygon with more than four sides?

A: If you have a polygon with more than four sides, you can break it down into smaller polygons, such as triangles or quadrilaterals, and then calculate the area of each smaller polygon. You can then add the areas together to find the total area of the larger polygon.

Q: What if I have a polygon with curved sides?

A: If you have a polygon with curved sides, you will need to use a different formula to calculate its area. The formula for finding the area of a polygon with curved sides is more complex and involves the use of calculus.

Q: Can I use a calculator to find the area of a polygon?

A: Yes, you can use a calculator to find the area of a polygon. Simply enter the base and height of the polygon into the calculator, and it will give you the area.

Q: What if I make a mistake when calculating the area of a polygon?

A: If you make a mistake when calculating the area of a polygon, you can try rechecking your work to see where you went wrong. You can also use a calculator to double-check your answer.

Q: Can I use the formula for finding the area of a polygon to find the area of a circle?

A: No, you cannot use the formula for finding the area of a polygon to find the area of a circle. The formula for finding the area of a circle is A = πr^2, where r is the radius of the circle.

Q: What is the difference between the area of a polygon and the perimeter of a polygon?

A: The area of a polygon is the amount of space inside the polygon, while the perimeter of a polygon is the distance around the polygon. The perimeter of a polygon is also known as the circumference of the polygon.

Q: Can I use the formula for finding the area of a polygon to find the area of a 3D shape?

A: No, you cannot use the formula for finding the area of a polygon to find the area of a 3D shape. The formula for finding the area of a 3D shape is more complex and involves the use of calculus.

Conclusion

In this article, we have answered some of the most frequently asked questions about finding the area of polygons. We hope that this article has been helpful in clarifying any confusion you may have had about finding the area of polygons. If you have any more questions, please don't hesitate to ask.

References

Math Open Reference. (n.d.). Polygon. Retrieved from https://www.mathopenref.com/polygon.html
Khan Academy. (n.d.). Area of a polygon. Retrieved from https://www.khanacademy.org/math/geometry/area-of-polygons/area-of-polygons/v/area-of-polygons

Glossary

Polygon: A two-dimensional shape with at least three sides and angles.
Quadrilateral: A polygon with four sides and angles.
Triangle: A polygon with three sides and angles.
Base: The length of the side of a polygon that is used to calculate its area.
Height: The length of the perpendicular line from the base of a polygon to its opposite vertex.
Area: The amount of space inside a two-dimensional shape.
Perimeter: The distance around a polygon.
Circumference: The distance around a circle.
Radius: The distance from the center of a circle to its edge.