10.4 Area and Circumference. 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 =

10.4Area and Circumference

Solving Area ProblemSolving Area Problem• Find the area of

polygon shown at right.• Solution:

A = (3)(13)f2 + (3)(6 + 3)f2

= 39f2 + 27f2

= 66 ft2

Area of a Area of a Parallelogram 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.

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Area of ParallelogramArea 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 = bhA = 8 cm ∙ 4 cm = 32 cm²

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Area of a TriangleArea of a Triangle• The area, A, of a triangle with height h and

base b is given by the formula

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Area of a TriangleArea of a Triangle

h

b

Using the Formula for a Triangle’s AreaUsing 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 bhA = ½ ∙ 16 m ∙ 10 m

= 80 m²

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Area of a TrapezoidArea of a Trapezoid• The area, A, of a trapezoid with parallel

bases a and b and with height h is given by the formula:

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Finding the Area of a TrapezoidFinding the Area of a Trapezoid

Find the area of the trapezoid.

Solution: The height is 13 ft. Thelower 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

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CircleCircle• 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.

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dr

Definition of Definition of ππ

dC

Area of a CircleArea of a Circle• A = πr2

• Find the area of a circle whosediameter is 12 in.

A = πr2 = π(12in)2 = (3.14)(144in2) ≈ 452.2 in2

dC r

ExampleExample• 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/in2.

Large pizza: A = πr2 = π (8 in.)2 = 64 π in2 ≈ 201 in2

Medium pizza: A = πr2 = π (4 in.)2 = 64π in2 ≈ 50 in2

Example (cont.)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,

2 2 2

$15.00 $15.00 $0.07

64 in. 201 in. in.

2 2 2

$7.50 $7.50 $0.15

16 in. 50 in. in.

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