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Lesson 15 Perimeter and Area

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Two important measurements you will be expected to find on the Terra Nova are the distance around a figure and the area the figure takes up. This lesson will give you the formulas you will need to know in order to determine those measurements.

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Perimeter A polygon is a closed figure made up of straight sides. Perimeter is the name mathematicians use for the distance around a polygon. Perimeter is determined by adding up the lengths of all the sides. In some cases, you can use a formula as a shortcut to adding and get the perimeter of a figure.

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Triangle p = a + b + c (where p = perimeter and a, b, and c are the lengths of the sides). a b c

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Square p = 4s (where s = the length of a side). s s

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Rectangle p = 2L + 2W (where L = length and W = width). W L

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Example 1 What is the perimeter of a triangle whose sides are 5, 12, and 13? Strategy: See if there is any shortcut formula for the perimeter. If not, add the lengths of the sides. There is no shortcut formula so add the lengths of the sides. 5 + 12 + 13 = 30

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Solution The perimeter of the triangle is 30.

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Example 2 The Chesterfield Middle School has a continuous row of shrubs around the front lawn, which is shaped like a rectangle. The front lawn is 55 feet wide and 24 feet long. How long is the row of shrubs?

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Strategy: See if there is a shortcut formula for the perimeter. If not, add the lengths of the sides. The perimeter of a rectangle has a shortcut formula. It is p = 2L + 2W. Substitute 55 for W and 24 for L into the formula: p = 2(24) + 2(55) = p = 48 + 110 p = 48 + 110

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Example 3 The perimeter of a square end table is 64 inches. What is the length of one side of the table? Strategy: See if there is a shortcut formula for the perimeter you can use. The perimeter of a square has the formula p = 4s. Substitute 64 for p. 64 = 4s. Divide both sides by 4, s = 16

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Solution The length of one side of the table is 16 inches.

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Circumference of a Circle See lesson 18, Properties of Circles, for basic definitions of the parts of circles. The distance around a circle is called its circumference. C = 2 r (where C = circumference, r = radius, and 3.14 or 22/7). r

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Solution The row of shrubs is 158 feet long.

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Example 4 A circular pond in a garden has a radius of 7 feet. What is its circumference. Strategy: Substitute the numbers into the formula for circumference. Step 1: Use the formula for the circumference of a circle: C = 2 r Step 2: Substitute the radius (7 feet) and (22/7 or 3.14) into the problem. C = (2) (22/7) (7) C = (2) (22/7) (7)

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Solution C = 44 feet

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Area of Triangles, Squares, and Rectangles The following are the formulas for the area of polygons that you need to know. Learn them. Keep a formula card in your notebook.

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Triangle A = ½ bh (where A = area, b = base, and h = height or altitude). b h

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Square A = s 2 (where s = side) s s

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Rectangle A = bh (where b = base and h = height). b h

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Example 5 Desks at the middle school are 24 inches by 14 inches. What is the area of the desk? Strategy: Substitute the numbers into the area formula. Substitute 24 for L and 14 for W and multiply. 24 x 14 = 336 in. 2

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Solution The area of each desk is 336 square inches. Area is always measured in square units.

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Example 6 Find the area of the triangle shown here. Strategy: Substitute the base and height into the area formula for triangles. 12 cm 8 cm

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A = ½ bh base = 12; height = 8 A = ½ x 12 x 8 = A = 48

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Solution The area of the circle is 48 sq. cm.

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Area of a Circle You should know the formula for the area of a circle: A = r 2 (where A = area, r = radius, and = 3.14 or 22/7). r

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Example 7 A circular pond has a radius of 7 feet. What is the area? Strategy: Substitute the numbers into the formula for area of a circle. Step 1: Use the formula A = r 2. Step 2: Substitute the radius (7 feet) and (22/7) into the formula.

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A = r 2 A = (22/7)(7 2 ) A = 22 x 7 x 7 7 A = 22 x 7 A = 54

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Solution The area of the circle is 154 square feet.

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C = (2 ) (22/7) (7)

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