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Section 9.3 Perimeter and Area

Section 9.3 Perimeter and Area. Definitions. The perimeter, P , of a two-dimensional figure is the sum of the lengths of the sides of the figure. The area, A , is the region within the boundaries of the figure. Formulas. Example 1: Sodding a Lacrosse Field.

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Section 9.3 Perimeter and Area

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  1. Section 9.3Perimeter and Area

  2. Definitions • The perimeter, P, of a two-dimensional figure is the sum of the lengths of the sides of the figure. • The area, A, is the region within the boundaries of the figure.

  3. Formulas

  4. Example 1: Sodding a Lacrosse Field Rob Marshall wishes to replace the grass (sod) on a lacrosse field. One pallet of Bethel Farms sod costs $175 and covers 450 square feet. If the area to be covered is a rectangle with a length of 330 feet and a width of 270 feet, determine a) The area to be covered with sod.

  5. Example 1: Sodding a Lacrosse Field a) the area to be covered with sod. Solution • A = l•w = 330 • 270 = 89,100 ft2

  6. Example 1: Sodding a Lacrosse Field b) Determine how many pallets of sod Rob needs to purchase. Solution Rob needs 198 pallets of sod.

  7. Example 1: Sodding a Lacrosse Field c) Determine the cost of the sod purchased. Solution The cost of 198 pallets of sod is 198 × $175, or $34,650.

  8. c a b Pythagorean Theorem The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. leg2 + leg2 = hypotenuse2 Symbolically, if a and b represent the lengths of the legs and c represents the length of the hypotenuse (the side opposite the right angle), then a2 + b2 = c2

  9. Example 2: Crossing a Moat • The moat surrounding a castle is 18 ft wide and the wall by the moat of the castle is 24 ft high (see Figure). If an invading army wishes • to use a ladder to • cross the moat andreach the top of thewall, how long mustthe ladder be?

  10. Example 2: Crossing a Moat • Solution The ladder needs to be at least 30 ft long.

  11. Circles • A circle is a set of points equidistant from a fixed point called the center. • A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. • A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. r d circumference

  12. Circles • The circumference is the length of the simple closed curve that forms the circle. r d circumference

  13. Example 4: Determining the Shaded Area Determine the shaded area. Use the π key on your calculator and round your answer to the nearest hundredth.

  14. Example 4: Determining the Shaded Area Solution Height of parallelogram is diameter of circle: 4 ft

  15. Example 4: Determining the Shaded Area Solution Area of parallelogram = bh = 10• 4 = 40 ft2 Area of circle = πr2 = π(2)2 = 4π ≈ 12.57 ft2

  16. Example 4: Determining the Shaded Area Solution Area of shaded region = Area of parallelogram – Area of circle • Area of shaded region ≈ 40 – 12.57 • Area of shaded region ≈ 27.43 ft2

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