# Math Area Formulas: Finding the Area of Geometric Shapes

By Robyn Broyles

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 = πr²

a = πd

Remember that ½d 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

a = 1π

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 = πd

a = π(½(6))²

a = π(3)²

a = 9π 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 = s²

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 = ½bh

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