![]() (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:Ī(lateral) = (s × (arc length)) / 2 = (s × 2 × π × r) / 2 = π × r × s The arc length of the sector is equal to 2 × π × r. It's a circular sector, which is the part of a circle with radius s ( s is the cone's slant height).įor the circle with radius s, the circumference is equal to 2 × π × s. 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. Try it out for yourself and see how easy it can be to find the area of a trapezoid, no matter what information you have available.Our surface area calculator can find the surface area of seven different solids. ![]() ConclusionĬalculating the area of a trapezoid can be a daunting task, but with the formulas and calculator we've provided, it doesn't have to be. The calculator will automatically calculate the area for you. Simply select the method that corresponds to the information you have available and enter the values in the appropriate boxes. Our trapezoid area calculator makes it easy to find the area of your trapezoid. If you know the lengths of the two diagonals and the angle between them, you can use the following formula to find the area of a trapezoid: S = \dfrac Using the Trapezoid Area Calculator Here are the formulas for calculating the area of a trapezoid based on different information: Area of Trapezoid by Diagonals and Angle That's why we've created this trapezoid area calculator – to make it easy for you to find the area of a trapezoid no matter what information you have. ![]() Calculating the area of a trapezoid can be challenging, especially if you don't have a lot of experience with geometry.
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