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10.4 Area and Circumference

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Solving Area Problem Find the area of polygon shown at right. Solution: A = (3)(13)f 2 + (3)(6 + 3)f 2 = 39f 2 + 27f 2 = 66 ft 2

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Area of a Parallelogram The area, A, of a parallelogram with height h and base b is given by the formula A = bh. The height of a parallelogram is the perpendicular distance between two of the parallel sides. It is not the length of a side. 3

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Area of Parallelogram Find the area of the parallelogram. Solution: The base is 8 centimeters and the height is 4 centimeters. Thus, b = 8 and h = 4. A = bh A = 8 cm ∙ 4 cm = 32 cm² 4

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Area of a Triangle The area, A, of a triangle with height h and base b is given by the formula 5

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Area of a Triangle h b

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Using the Formula for a Triangle’s Area Find the area of the triangle. Solution: The base is 16 meters and the height is 10 meters. Thus, b = 16 and h = 10. A = ½ bh A = ½ ∙ 16 m ∙ 10 m = 80 m² 7

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Area of a Trapezoid The area, A, of a trapezoid with parallel bases a and b and with height h is given by the formula: 8

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Finding the Area of a Trapezoid Find the area of the trapezoid. Solution: The height is 13 ft. The lower base, a, is 46 ft and the upper base, b, is 32 ft. Thus, A = ½h(a +b). A = ½ ∙ 13 ft ∙ (46 ft + 32 ft) = 507 ft² 9

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Circle Circle -- a set of points in the plane equally distant from a given point, its center. Radius -- a line segment from the center to any point on the circle. All radii in a given circle have the same length. Diameter -- a line segment through the center whose endpoints both lie on the circle. It is twice the radius. 10 d r

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Definition of π d C

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Area of a Circle A = πr 2 Find the area of a circle whose diameter is 12 in. A = πr 2 = π(12in) 2 = (3.14)(144in 2 ) ≈ 452.2 in 2 d C r

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Example Which is a better buy? A large pizza with a 16-in diameter for $15.00 or a medium pizza with an 8-in diameter for $7.50? Compare price/in 2. Large pizza: A = πr 2 = π (8 in.) 2 = 64 π in 2 ≈ 201 in 2 Medium pizza: A = πr 2 = π (4 in.) 2 = 64π in 2 ≈ 50 in 2

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Example (cont.) Price per square inch: Price per square inch for large pizza = Price per square inch for medium pizza = The large pizza is the better buy, 14

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