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How to Find Polynomials for Perimeters & Areas

Word problems commonly call for students to find the area or perimeter of a specific shape. It provides specific numerical values for lengths and widths. A polynomial formula takes those values and sets them equal to a perimeter or area. Using inverse operations, the values move from one side of the equation to the other to eventually isolate x on one side of the equation with its value on the other. Different geometric shapes have formulas particular to their characteristics for finding perimeter and area. Therefore, it helps to have a good understanding of word problems and modeling.

Instructions

  1. The Basic Steps for Finding a Polynomial Equation

    • 1

      Read the following problem: The length of one side of a rectangle is 29 feet. The width of one side of the rectangle is 33 feet. What is the perimeter and the area for the rectangle?

    • 2

      Set up a polynomial formula with the situational values for the perimeter. The formula for perimeter is P = 2L + 2W; the perimeter equals two times the length plus two times the width.

    • 3

      Plug in the values. The perimeter is unknown, so use P to represent it. The length is 29 and the width is 33. The polynomial formula for the perimeter is P = 2(29) + 2(33).

    Solving to Find Perimeter and Area

    • 4

      Apply the distributive property to solve for the parentheses: (2 x 29) + (2 x 33) = 58 + 66. Simplify the formula: P = 124. The perimeter is 124 feet.

    • 5

      Set up a polynomial formula for the area of the rectangle. The formula is A = LW, or area equals length times width. Plug in the values: A = 29 x 33.

    • 6

      Simplify the equation: A = 957. The area of the rectangle is 957 square feet.

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