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Understanding Perimeter and Area of Rectangles and Squares: Formulas and Examples

This guide covers the concepts of perimeter and area specifically for rectangles and squares. A square has four equal sides, and its perimeter is calculated as P = 4s, where s is the side length. For rectangles, with two pairs of opposite equal sides, the perimeter is given by P = 2(l + w) or P = 2l + 2w, where l is the length and w is the width. Examples include calculating the perimeter of a field and the area of specific shapes, illustrating how to apply these formulas with real-world dimensions.

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Understanding Perimeter and Area of Rectangles and Squares: Formulas and Examples

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  1. § 7.2 Rectangles and Squares

  2. 5 A square has four equal sides. 5 5 5 Perimeter of a Rectangle A rectangle has two adjoining perpendicular sides, and the lengths of the opposite sides are equal. 9 5 5 9 The perimeter (P) of a rectangle is the sum of the lengths of all its sides. P = 5 + 9 + 5 + 9 = 28 P = w + l + w + l = 2l + 2w

  3. Perimeter of a Rectangle Example: Find the perimeter of a field that is 6 miles long and 3.5 miles wide. P = 2l + 2w = 2(6) + 2(3.5) = 12 + 7 = 19 The field has a perimeter of 19 miles.

  4. 3.25 in 3.25 in 3.25 in 3.25 in Perimeter of a Square The perimeter (P) of a square is four times the length of a side. P = 4s Example: Find the perimeter of the following square. P = 4s = 4(3.25) = 13 The perimeter is 13 inches.

  5. 5.65 ft 0.95 ft Add all of the sides. 0.25 ft 3 ft 1.2 ft 3.8 ft Perimeters of Shapes Example: Find the perimeter of the following shape. 5.65 0.95 0.25 1.2 3.8 3 14.85 The perimeter is 14.85 feet.

  6. All areas are measured in square units. Area of a Rectangle The area (A)of a rectangle is the length times the width. A = lw Example: Find the area of a field that is 6 miles long and 3.5 miles wide. A = lw = (6)(3.5) = 21 square miles (or 21 mi2)

  7. 3.25 in 3.25 in 3.25 in 3.25 in Area of a Square The area (A)of a square is the square of the length of one side. A = s2 Example: Find the area of the following square. A = s2 =3.252 = 10.5625 in2

  8. 2.25 ft 3.25 ft 1.95 ft 2.25 ft 1.75 ft 1.75 ft 3.8 ft Area of Shapes Example: Find the area of the following shape. A = 0.252 + A = (3.25)(1.95) + A = (1.75)(3.8) = 0.0625 + 6.3375 + 6.65 = 13.05 ft2

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