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Unit 26

Unit 26. AREAS OF COMMON POLYGONS. 7 in. 3.5 in. AREAS OF RECTANGLES. A rectangle is a four-sided polygon with opposite sides equal and parallel and with each angle equal to a right angle The area of a rectangle is equal to the length times the width

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Unit 26

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  1. Unit 26 AREAS OF COMMON POLYGONS

  2. 7 in 3.5 in AREAS OF RECTANGLES • A rectangle is a four-sided polygon with opposite sides equal and parallel and with each angle equal to a right angle • The area of a rectangle is equal to the length times the width • Determine the area of the figure shown below: • Area = length  width = 7 in  3.5 in = 24.5 square inches Ans

  3. AREAS OF PARALLELOGRAMS • A parallelogram is a four-sided polygon with opposite sides parallel and equal • The area of a parallelogram is equal to the product of the base and height Area = base × height

  4. AREAS OF PARALLELOGRAMS • Find the base of a parallelogram given that its area is 164 square meters and its height is 16 meters: • Area = base  height Substitute in the given measurements and transpose the formula for the base 164 m2 = b 16 m b = 10.25 m Ans

  5. AREAS OF TRAPEZOIDS • A trapezoid is a four-sided polygon that has only two sides parallel • Common trapezoids • Ramps (loading and jumping) • Utility knife blades • Door stops (some not all) • The area of a trapezoid is equal to one half the product of the height and the sum of the bases Area = ½(b1 + b2)h

  6. 10.25 ft 4.75ft 8.5 ft AREAS OF TRAPEZOIDS (Cont) • Find the cross sectional area of the hot tub shown below • Area = ½ (b1 + b2) h = 44.53 ft2 Ans

  7. AREAS OF TRIANGLES • The area of a triangle is equal to one-half the product of the base and height • Determine the area of the gable end of your home: - Notice the isosceles triangle, so use Pythagorean Theorem to get your height. • Area = 1/2 the base times the height 15.5 m = 1/2 (26.75 m)(15.5 m) = 104.73 m2Ans 26.75 m

  8. AREAS OF TRIANGLES GIVEN THREE SIDES • When three sides of a triangle are known and the height is unknown, Hero’s (Heron’s) Formula can be used to determine its area Where: A = area; a, b, and c = sides; and s = 1/2 (a + b + c)

  9. AREAS OF TRIANGLES GIVEN THREE SIDES • Find the area of a triangle with sides of 10m,16m, and 20m: Where: A = area; a, b, and c = sides; and s = 1/2 (a + b + c) • First find s: s = 1/2 (a + b + c) = 1/2 (10 m + 16 m + 20 m) = 23 m

  10. PRACTICE PROBLEMS • A rectangular piece of wood is 4 feet wide and 6.5 feet long. Find the area of the wood in square feet. • How much would the piece of wood in problem #1 cost if it sells for $0.12 per square foot? • Determine the height of a parallelogram given that it has an area of 153.9 square inches and a base of 16.2 inches.

  11. PRACTICE PROBLEMS (Cont) • The cross section of a wooden planter is in the shape of a trapezoid with a height of 486.9 cm and bases of 34.2 cm and 18.4 cm. Find the cross-sectional area of the planter in square centimeters. • Find the missing base of a trapezoid given that it has an area of 154 in2, a height of 8.8 in, and the known base is 14.2 inches. • Determine the height of a triangle given that it has an area of 100 square meters and a base of 6.25 meters.

  12. 7 in 5 in 8 in 14 in PRACTICE PROBLEMS (Cont) • Find the area of a triangle with sides of 12 mm, 15 mm, and 18 mm. • Determine the area of the end of a parking block pictured below:

  13. PROBLEM ANSWER KEY • 26 ft2 • $3.12 • 9.5 inches • 12805.47 cm2 • 20.8 inches • 32 meters • 89.294 mm2 • 164.5 in2

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