## 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 ft ^{2} **

** **

## How to Find the Area of a Square

Use the **A = a ^{2}**

^{ }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 = a^{2}

A = 12^{2}

**A = 144 in ^{2}**

## How to Find the Area of a Circle

To find the area of a circle, use the following formula: **A = πr ^{2}**. The “r” in this formula represents the radius

of the circle.

**Example**:

A = π 2

A

= 14π 2

A = π 196

**A ≈ 615.75 m**^{2}

^{ }

## 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 cm ^{2}**

^{ }

## 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 yd ^{2}**

** **

** **

## 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**

**ft**

^{2}** **

** **

## 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 in ^{2}**

^{ }

^{ }

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.