Surface area refers to the total area that an object’s surface occupies. It can also refer to the total area of a 3D object’s surface. Sometimes, you can split the surface area into the sum of the lateral surface area and the base area/s. Use this surface area calculator to find the surface area in an instant without having to perform calculations.
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How to use the surface area calculator?
When you’re learning how to calculate surface area, this surface area calculator comes in handy. Use it to check your answer or use it to perform the calculation for you. Here are the steps to follow for this online tool:
- First, choose the Shape from the drop-down menu.
- Then enter the value of the Length and choose the unit of measurement from the drop-down menu.
- The calculator then generates for you the value of the Surface Area along with an illustration of the shape you have chosen.
How to find the surface area of a rectangular prism?
When you learn how to calculate surface area, this applies to different shapes. This is why the surface area calculator is so useful. You can use it to find the surface area of the most common shapes. To find the surface area of a rectangular prism, first perform the calculations to find the areas of the rectangular sides:
A1 = l * w
A2 = w * h
A3 = l * h
The complete formula is:
A = 2 * (l * w + w * h + l * h)
when simplified is A = 2 * (A1 + A2 + A3)
How to find the surface area of a triangular prism?
Before we go to the formula for the surface area of a triangular prism, you must first understand where it’s derived. For this shape, the lateral surface area is quite easy to calculate as it’s made up of 3 rectangles which have one length of the side in common. Therefore, the formula is:
A(lateral) = a * h + b * h + c * h = h * (a + b + c)
when simplified is A(lateral) = h * P
where
P refers to the perimeter of the base triangle
After this, it’s time to calculate the area of the triangular base. There are several ways to do this depending on the value you have. One of the most common methods is to use Heron’s formula which is typically used when you have the values for all three sides of the triangle. For this, the formula is:
A(base) = 0.25 * √((a + b + c) * (-a + b + c) * (a – b + c) * (a + b – c)))
Therefore, the final formula to use to find a triangular prism’s surface area is:
A = h * (a + b + c) + 0.5 * √((a + b + c) * (-a + b + c) * (a – b + c) * (a + b – c))
when simplified is A = A(lateral) + 2 * A(base)
How to find the surface area of a cylinder?
To solve for the surface area of a cylinder, you need to have two values which are the height and the diameter or radius of the base. Generally, the formula for the base of a circle is:
A = 2πr² + 2πrh
This formula comes from the equation of a cylinder’s surface area which is:
A = A(lateral) + 2 * A(base)
To use this formula, you must first find the base and lateral area using the following equations:
A(base) = π * r²
A(lateral) = h * (2 * π * r)
How to find the surface area of a cube?
Among all of the shapes, the surface area of a cube is the easiest one to find. You won’t even need to use a surface area calculator for this. Since the formula for the surface area of a square is:
A = 6 * (side area)
The area of the square equals the product of the length of all of its sides. Therefore, the formula for the surface area of a cube is:
A = 6 * l²
where
l refers to one side of the square
How to find the surface area of a pyramid?
A pyramid is a 3D shape with triangular lateral faces and a polygonal base. Usually, pyramids usually have a regular polygon base. This is the type of pyramid we will use for this particular surface area calculation. The formula to use is:
A = l * √(l² + 4 * h²) + l²
where
l refers to a base side
h refers to the pyramid’s height
From this, you can split the formula into:
A = A(base) + A(lateral) = A(base) + 4 * A(lateral face)
The base refers to the square shape, therefore:
A(base) = l²
When you calculate the lateral surface area, begin with the area of one of the triangular faces. To find the triangle’s height, use for hypotenuse formula which is:
c = √(a² + b²)
Calculate the ABC hypotenuse of the triangle using the formula:
c = √(h² + (l/2)²) = √(h² + l²/4)
In this case, you can calculate the area of the triangle using the formula:
A = height * base / 2 so
A(lateral face) = √(h² + l²/4) * l / 2
Therefore, the final formula you can use to calculate the surface area of a pyramid is:
A = l² + 4 * √(h² + l²/4) * l / 2 = l² + 2 * l * √(h² + l²/4)
when simplified is A = l² + l * √(4 * h² + l²)
How to find the surface area of a sphere?
If you need to solve for the surface area of a sphere, you must first know its diameter or radius because the formula for the surface area is:
A = 4 * π * r²
where
r refers to the radius
Since the diameter of a sphere equals two radii or d = 2r, you can use another form of the equation which is:
A = 4 * π * (d / 2)² = π * d²
where
d refers to the diameter of the sphere
