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Math Area Formulas: Finding the Area of Geometric Shapes

written by: Robyn Broyles • edited by: SForsyth • updated: 9/11/2012

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 = 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

  • 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 = 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

  • 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 = 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