# Math Area Formulas: Finding the Area of Geometric Shapes

Find formulas for the area of a circle, square, rectangle, and triangle. In this study guide, example "find area" problems are solved step-by-step to show how to use area formulas in geometry.

## Area of a Circle Formula

The formula for the area of a circle, where *a* is area, *d* is the diameter, and *r* is the radius, can be written two ways:

*a* = *πr*²

*a* = *π*(½*d*)²

Remember that ½*d* must be placed in parentheses in the second formula!

**Problem 1:**

The radius of a circle is 1 cm. What is the area? Use the value 3.14 for *π*.

*a* = *π*1²

*a* = 1*π*

*a* = 3.14 square centimeters

**Problem 2:**

The diameter of a circle is 6 feet. What is the area? Use 3.14 for *π*.

*a* = *π*(½*d*)²

*a* = *π*(½(6))²

*a* = *π*(3)²

*a* = 9*π a* = 28.26 square feet

## Area of a Square Formula

The formula for the area of a square, where *a* is area and *s* is the length of one of the sides, is

*a* = *s*²

** Problem:**

A square of carpet is 1.5 meters long on a side. What is its area?

*a* = 1.5²

*a* = 2.25 square meters

## Area of a Rectangle Formula

The formula for the area of a rectangle, where *a* is area, *w* is the width, and *h* is the height, is

*a* = *hw*

**Problem:**

A rectangular painting, with its frame, is 30 inches wide and 18 inches high. How much area does it cover on the wall?

*a* = (18)(30)

*a* = 540 square inches

## Area of a Triangle Formula

The formula for the area of a triangle, where *a* is the area, *b* is the length of the base (which can be any of the sides), and *h* is the height (measured perpendicular to the base), is

*a* = ½*bh*

In a right triangle, the base is one of the legs and the height is the other leg.

**Problem 1:**

A triangle has a base of 5 inches and a height of 20 inches. What is its area?

*a* = ½(5)(20)

*a* = ½(100)

*a* = 50 square inches

**Problem 2:**

A right triangle has legs of length 3 inches and 4 inches, respectively. What is its area?

*a* = ½(3)(4)

*a* = ½(12)

*a* = 6 square inches