Section 2.3 Formulas and Applications 75 In Objectives 2 and 3, we will solve problems that are modeled by known formulas. First we will work with formulas that deal with various geometric shapes and circles, namely, perimeter, area, and circumference. Definition: The perimeter of a polygon is the distance around the outside of the figure. In other words, it is the sum of the lengths of the sides of the polygon. The distance around a circle is called the circumference of the circle. Definition: The area of a figure is the number of square units it takes to cover the inside of the figure. (A square unit is a square whose length and width are both 1 unit long.) The perimeter and area formulas for some common shapes are as follows. Triangle B c h a A b C P = a + b + c A = 1 2 bh Rectangle w l P = 2l + 2w A = lw Square s P = 4s A = s2 Circle r C = 2πr or C = πd A = πr2 The perimeter, area, and circumference formulas will be used in two ways. In Example 2 parts (a)–(c), the dimensions of a geometric shape are known. We will calculate the area, perimeter, and/or circumference by substituting the given dimensions into the appropriate formula. In Example 2 parts (d)–(e), the perimeter or area is known as is one of the shape’s dimensions. The known values must be substituted into the appropriate formula. It will be necessary to solve the resulting equation to find the unknown dimension. Objective 2 Examples Use the perimeter, area, or circumference formulas to solve each problem. 2a. What is the perimeter and area of a rectangle whose length is 5 ft and whose width is 12 ft?
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