22 Apr How to Find the Area of a Shape. Formulas and Examples.

How to Find the Area of a Shape

The term
“area” in mathematics refers to the amount of space that a two-dimensional
shape occupies. Area can be represented by centimeters, meters, feet, and other
units of measurement. Because not all geometric 2D shapes have the same number
of sides, a different formula is required for calculating the area for each
shape. This page will focus on finding the area of seven of the most common 2D
shapes. These include rectangle, square, circle, triangle, trapezoid, ellipse, and parallelogram.

 

Because
these formulas involve 2D shapes, all area calculations have a “2” exponent
(also known as a superscript or power) to indicate that the shape has two
sides.

How to Find the Area of a Rectangle 

The formula
for finding the area of a rectangle is A
= w x l, where “w” represents the width and “l” represents the length.

Example:

A = w x l

A = 32 x 52

 

A = 1664 ft²

 

How to Find the Area of a Square

Use the A = a² formula
to find the area of a square. The “a” represents one side of the square. Since
a square has four equal sides, having the measurement of one side gives you the
measurement for the others.

  

Example:

 
A = a²

A = 12²

 

A = 144 in²

 

How to Find the Area of a Circle

To find the area of a circle, use the following formula: A = πr². The “r” in this formula represents the radius
of the circle.

Example:

A = π 2

A
= 14π 2

A = π 196

 

A ≈ 615.75 m²

 

How to Find the Area of a Triangle

The standard formula for finding the area of a triangle is  where “b” represents
the base and “h” represents the height. 

Example:

 

A = 58.5 cm²

 

How to Find the Area of a Trapezoid

Use
the formula to find the
area of a trapezoid. In this formula, “a” represents the shorter base (top),
“b” represents the longer base (bottom), and “h” represents the height.

 

Example:

 

A = 36 yd²

 

 

How to Find the Area of an Ellipse

An
ellipse is similar to a circle in its appearance, except that it is precisely
defined. It is, essentially, a circle, stretched horizontally, with two
symmetrical axes. An oval is not precisely
defined. To calculate the area of an ellipse, use the A = π a x b formula. The “a”
represents the horizontal axis while the “b” represents the vertical axis.

 

Example:

 

A
= π a x b

A
= π x 4 x 15

A
≈ 12.566 x 15

 

A
≈ 188.5 ft²

 

 

How to Find the Area of a Parallelogram

The
formula for calculating the area of a parallelogram is A = b x h. The “b” represents the base, and the “b” represents the
height.

 

Example:

 

 

A
= b x h

A
= 23 x 11

 

A = 253 in²

 

 

Area Formulas of Common Geometric Shapes

The chart below provides the area formula of the
aforementioned 2D shapes, in addition to some other common ones.