Math Area Formulas: Finding the Area of Geometric Shapes
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 = π(½d)²
Remember that ½d must be placed in parentheses in the second formula!
The radius of a circle is 1 cm. What is the area? Use the value 3.14 for π.
a = π1²
a = 1π
a = 3.14 square centimeters
The diameter of a circle is 6 feet. What is the area? Use 3.14 for π.
a = π(½d)²
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
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
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.
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
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