Surface area formulas in geometry refer to the lateral surface and total surface areas of different geometrical objects. To recall, the surface area of an object is the total area of the outside surfaces of the three-dimensional object i.e, the total sum of the area of the faces of the object. It is measured in terms of square units. In other words, the surface area is the sum of all the areas of all the shapes that cover the surface of the object. On the other hand, the lateral surface area refers to the area of the sides of a shape, excluding its base and top area. Show
Try Various Surface Area Calculators Here: Maths Calculators Here in this page, you can see a list of Surface Area Formulas for all kinds of available geometrical figures. Surface Area Formulas:
Download This Formula Sheet for Surface Areas: Check More Formulas for Surface Areas
Related Pages The following table gives the surface area formulas for solid shapes or three-dimensional shapes. Scroll down the page if you need more explanations about the formulas, how to use them as well as worksheets. Surface Area Of A CubeA cube is a three-dimensional figure with six equal square sides. The figure below shows a cube with sides s. If s is the length of one of its sides, then the area of each side of a cube is s2.
Since a cube has six square-shape sides, its total surface area is 6 times s2. Worksheets and More Examples: How to find the surface area of a cube using the formula? Example:
Rectangular Solid Or CuboidsA rectangular solid is also called a rectangular prism or a cuboid. In a rectangular solid, the length, width and height may be of different lengths. The surface area of the above cuboid would be the sum of the area of all the surfaces which are
rectangles. Total area of front and back surfaces is lh + lh = 2lh Total area of the two side surfaces is wh + wh = 2wh Surface area of rectangular solid = 2lw + 2lh + 2wh = 2(lw + lh + wh) Worksheets and More Examples on Rectangular Prisms: How to find the surface area of a rectangular prism or cuboid? Example:
Surface Area Of PrismA prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. The other faces are in the shape of rectangles. They are called lateral faces. A prism is named after the shape of its base. The surface area of a prism is the sum of the area of all its external faces. We can also use the formula: Worksheets and More Examples: How to find the surface area of a triangular prism by adding the area of the external faces?
How to find the surface area of a triangular prism using the formula SA = ab+(s1+s2+s3)h? where a = altitude (height of the triangular face) b = base of triangle h = height of prism or distance between the two triangular faces. s1, s2 and s3 are the three sides of the triangle
Surface Area Of SphereA sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The distance from the center to the surface is the radius. Surface area of a sphere with radius r = 4 πr2 Worksheets and More Examples: How to find the surface area of a sphere? Example:
Surface Area Of Solid CylinderA cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases. The net of a solid cylinder consists of 2 circles and one rectangle. The curved surface opens up to form a rectangle. Surface area = 2 × area of circle + area of rectangle Surface Area = 2πr2 + 2πrh = 2πr (r + h) Worksheets and More Examples: How to find the surface area of a cylinder? Example:
Surface Area Of Hollow CylinderSometimes you may be required to calculate the total surface area of a hollow cylinder or tube. Total surface area of hollow cylinder = 2πrh + 2πRh + 2(πR2 − πr2) Surface Area Of ConeA cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex. The net of a solid cone consists of a small circle and a sector of a larger circle. The arc of the sector has the same length as the circumference of the smaller circle. Surface area of cone = Area of sector + area of circle Worksheets and More Examples: How to find the surface area of a cone? Example:
Surface Area Of PyramidA pyramid is a solid with a polygonal base and several triangular lateral faces. The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. A pyramid is named after the shape of its base. A rectangular pyramid has a rectangle base. A triangular pyramid has a triangle base. We can find the surface area of any pyramid by adding up the areas of its lateral faces and its base. Surface area of any pyramid = area of base + area of each of the lateral faces If the pyramid is a regular pyramid, we can use the formula for the surface area of a regular pyramid.
If the pyramid is a square pyramid, we can use the formula for the surface area of a square pyramid. Surface area of square pyramid = b2 + 2bs Worksheets and More Examples on Rectangular Prisms: How to find the surface area of regular pyramid? Example:
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