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SURFACE AREA OF A PRISM HOW TO

The other word that will come up regularly in our formulas is height. For example, if you have a hexagonal prism, the bases are the two hexagons on either end of the prism. The bases of a prism are the two unique sides that the prism is named for. The first word we need to define is base.

SURFACE AREA OF A PRISM HOW TO

The base is in the shape of a square, so A(base) = l².Hi, and welcome to this video on finding the Volume and Surface Area of a Prism!īefore we jump into how to find the volume and surface area of a prism, let’s go over a few key terms that we will see in our formulas. A = A(base) + A(lateral) = A(base) + 4 * A(lateral face).A = l * √(l² + 4 * h²) + l² where l is a base side and h is a height of a pyramid.The formula for surface area of a pyramid is: That's the option that we used as a pyramid in this surface area calculator. Regular means that it has a regular polygon base and is a right pyramid (apex directly above the centroid of its base) and square - that it has this shape as a base. But depending on the shape of the base, it could also be a hexagonal pyramid or a rectangular pyramid one. When you hear a pyramid, it's usually assumed to be a regular square pyramid. A = π * r * √(r² + h²) + π * r² given r and h.Ī pyramid is a 3D solid with a polygonal base and triangular lateral faces.A = A(lateral) + A(base) = π * r * s + π * r² given r and s or.Finally, add the areas of the base and the lateral part to find the final formula for surface area of a cone:.Thus, the lateral surface area formula looks as follows: r² + h²= s² so taking the square root we got s = √(r² + h²).But that's not a problem at all! We can easily transform the formula using Pythagorean theorem: Usually, we don't have the s value given but h, which is the cone's height.(sector area) = (π * s²) * (2 * π * r) / (2 * π * s)įor finding the missing term of this ratio, you can try out our ratio calculator, too!

(sector area) / (large circle area) = (arc length) / (large circle circumference) so: The formula can be obtained from proportions, as the ratio of the areas of the shapes is the same as the ratio of the arc length to the circumference:

The area of a sector - which is our lateral surface of a cone - is given by the formula:.

The arc length of the sector is equal to 2 * π * r.

For the circle with radius s, the circumference is equal to 2 * π * s.

It's a circular sector, which is the part of a circle with radius s ( s is the cone's slant height). Let's have a look at this step by step derivation: The base is again the area of a circle A(base) = π * r², but the lateral surface area origins maybe not so obvious:

A = A(lateral) + A(base), as we have only one base, in contrast to a cylinder.

We may split the surface area of a cone into two parts:

Surface area of a pyramid: A = l * √(l² + 4 * h²) + l², where l is a side length of the square base and h is a height of a pyramid.īut where do those formulas come from? How to find the surface area of the basic 3D shapes? Keep reading, and you'll find out!.

Surface area of a triangular prism: A = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) + h * (a + b + c), where a, b and c are the lengths of three sides of the triangular prism base and h is a height (length) of the prism.

Surface area of a rectangular prism (box): A = 2(ab + bc + ac), where a, b and c are the lengths of three sides of the cuboid.Surface area of a cone: A = πr² + πr√(r² + h²), where r is the radius and h is the height of the cone.Surface area of a cylinder: A = 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.Surface area of a cube: A = 6a², where a is the side length.Surface area of a sphere: A = 4πr², where r stands for the radius of the sphere.The formula depends on the type of solid. Our surface area calculator can find the surface area of seven different solids.