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.

- slide 1 of 4
### 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*)²Remember 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 - slide 2 of 4
### 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 - slide 3 of 4
### 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 - slide 4 of 4
### 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