Pyramid Area Calculator
Area
Pyramid
Pyramid area
If you're trying to find the area of a pyramid, you've come to the right place. Our pyramid area calculator can help you quickly calculate the surface area of different types of pyramids. It's easy to use - just enter the required values into the calculator and let it do the work for you.
Pyramid Area Formula
A pyramid is a three-dimensional shape with a polygonal base and a point called the apex. The area of a pyramid is the total area of all its faces. The formula for finding the area of a pyramid depends on the shape of its base. Here are the formulas for some of the most common types of pyramids.
Total surface area of the regular pyramid across the height.
The total surface area of the regular pyramid is the sum of the area of base and the area of the lateral surface.
S = \dfrac{na}{2}\left(\dfrac{a}{2tg\left(\dfrac{180^o}{n}\right)}+\sqrt{h^2+\left(\dfrac{a}{2tg\left(\dfrac{180^o}{n}\right)}\right)^2}\right)where S is the area, n is the qty of pyramid base sides , a is the length of the base side, h is the slant height of the pyramid.
Lateral surface area of the regular pyramid through the height
A pyramid is considered correct if its base is a regular polygon at, it follows that all its edges are equal to each other, if the height of the pyramid is known, then in order to find the area you first need to calculate the apothem, this is possible by Pythagorean theorem, since by connecting the height and the apothem we get a right triangle. Substituting, we obtain the formula of the area of the lateral surface of the pyramid through the height.
S = \dfrac{na}{2}\sqrt{h^2+\left(\dfrac{a}{2tg\left(\dfrac{180}{n}\right)}\right)^2}where S is the area, n is the qty of pyramid base sides , a is the length of the base side, h is the slant height of the pyramid.
Lateral surface area of the regular pyramid through the apothem
The area of the lateral surface of a regular pyramid is equal to the sum of the areas of its faces, the number of faces depends on the n-number of sides of the polygon at the base. The area of each face is calculated according to the formula of the area of isosceles triangle where the apothem of the pyramid serves instead of height.
S = \dfrac{1}{2}pfwhere S is the area, p is the perimeter of the base, and f is the apothem of the pyramid.
How to Use the Pyramid Area Calculator
Our pyramid area calculator makes it easy to find the area of your pyramid. To use the calculator:
- Select the type of surface area you want to calculate (lateral surface area or total surface area)
- Enter the dimensions of your pyramid.
- Our calculator will automatically calculate the area of your pyramid.
Examples of Finding Pyramid Area
Here are some examples of finding the area of a pyramid using the formula:
Example 1
Find the lateral surface area of a pyramid with a square base of length 4 and a height of 6.
S = \dfrac{na}{2}\sqrt{h^2+\left(\dfrac{a}{2tg\left(\dfrac{180}{n}\right)}\right)^2}S = \dfrac{4*4}{2}\sqrt{6^2+\left(\dfrac{4}{2tg\left(\dfrac{180}{4}\right)}\right)^2}S = 50.6Example 2
Find the total surface area of a pyramid with a hexagonal base of side length 5 and a height of 8.
S = \dfrac{na}{2}\left(\dfrac{a}{2tg\left(\dfrac{180^o}{n}\right)}+\sqrt{h^2+\left(\dfrac{a}{2tg\left(\dfrac{180^o}{n}\right)}\right)^2}\right)S = \dfrac{6*5}{2}\left(\dfrac{5}{2tg\left(\dfrac{180^o}{6}\right)}+\sqrt{8^2+\left(\dfrac{5}{2tg\left(\dfrac{180^o}{6}\right)}\right)^2}\right)S = 201.4Conclusion
Calculating the area of a pyramid is an important skill in geometry. Our pyramid area calculator and formula make it easy to find the area of your pyramid. Try it out for yourself and see how easy it can be!
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