How to Calculate the Area of a Base

How to Calculate the Area of a Base
••• gbarm/iStock/GettyImages

In geometry, the bottom of a three-dimensional object is called a base – if the top of the solid is parallel to the bottom it is also called a base. Since bases occupy a single plane, they have only two dimensions. You can find the area of a base by using the formula for the area of that shape.

Square Bases

Cubes and square pyramids have bases that are square-shaped. The area of a square is equal to the length of one of its sides multiplied by itself, or squared. The formula is A = s2. For example, to find the area of a base of a cube with 5-inch sides: A = 5 inches x 5 inches = 25 square inches

Rectangular Bases

Some rectangular solids and pyramids have rectangular bases. The area of a rectangle is equal to its length, l, multiplied by its width, w: A = l x w. Given a pyramid whose base is 10 inches long and 15 inches wide, find area as follows: A = 10 inches x 15 inches = 150 square inches.

Circular Bases

The bases of cylinders and cones are circular. The area of a circle is equal to the circle's radius, r, squared then multiplied by a constant called pi: A = pi x r2. Pi always has the same value, approximately 3.14. While pi technically has an endless number of decimal places, 3.14 is a good enough estimation for simple calculations. For example, given a cylinder with a radius of 2 inches, you can find the base's area as follows: A = 3.14 x 2 inches x 2 inches = 12.56 square inches.

Triangular Bases

A triangular prism has a triangular base. Finding a triangle's area requires two known quantities: base, labeled b, and height, labeled h. Base is the length of one of the triangle's sides, height is the distance from that side to the opposite corner of the triangle. The area of the triangle is equal to half of the base times the height: A = b x h x 1/2 You could find the area of a triangle with base length of 4 inches and height of 3 inches as follows: A = 4 inches x 3 inches x 1/2 = 6 square inches.

Related Articles

How to Calculate Lateral Area
How to Calculate the Base of a Cone
How to Find the Surface Area of a Triangular Prism...
How to Calculate Area in Square Inches
How to Calculate Height From Volume
How to Find the Total Surface Area of a Closed Cylinder
Math Equations for Volume & Surface Area
How to Find the Height of a Prism
How to Find the Height of a Rhombus
How to Find the Area of Triangles & Trapezoids
How to Calculate the Volume and Circumference of a...
How to Solve a Hexagon
How to Find the Volume of a Triangular Pyramid
How to Find the Radius of a Cone
How to Find the Volume of a Parallelogram
How to Calculate the Area of a Curved Surface
How to Calculate the Surface Area of a Cylinder
How to Calculate Triangles
How to Find Angles in a Trapezoid
How to Calculate the Volume of a Cylinder

Dont Go!

We Have More Great Sciencing Articles!