Chapter Area, Pythagorean Theorem, and Volume 14 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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Presentation transcript:

Chapter Area, Pythagorean Theorem, and Volume 14 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

14-1 Areas of Polygons and Circles  Areas on a Geoboard  Converting Units of Area  Land Measure  Area of a Rectangle  Area of a Parallelogram  Area of a Triangle  Area of a Kite  Area of a Trapezoid  Area of a Regular Polygon  Area of a Circle  Area of a Sector Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Areas on a Geoboard Addition method divide an area into smaller pieces and then add the areas. What is the area of this figure? 19 square units Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Rectangle method – construct a rectangle encompassing the entire figure and then subtract the areas of the unshaded regions.  Area = 16 – ( ) = 9 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 14-1 Find the area of the figure. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 14-1 The area of the hexagon equals the area of the surrounding rectangle minus the sum of the areas of figures a, b, c, d, e, f, and g. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Converting Metric Units of Area UnitSymbol Relationship to Square Meter square kilometerkm 2 1,000,000 m 2 square hectometerhm 2 10,000 m 2 square dekameterdam m 2 square meterm2m2 base unit square decimeterdm m 2 square centimetercm m 2 square millimetermm m 2 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Convert each of the following: a.5 cm 2 to mm 2 Example 14-2 b. 124,000,000 m 2 to km 2 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

UnitEquivalent of Other Units 1 ft in. 2 or yd 2 1 yd 2 9 ft 2 1 mi 2 3,097,600 yd 2 or 27,878,400 ft 2 Converting English Units of Area Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Land Measure English units acre square mile Metric units are hectare square kilometer Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Unit of AreaEquivalent of Other Units 1 a100 m 2 1 ha100 a, or 10,000 m 2, or 1 hm 2 1 km 2 1,000,000 m 2 1 acre4840 yd 2 1 mi acres Land Measure Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

a.A square field has a side of 400 m. Find the area of the field in hectares. Example 14-3 b. A square field has a side of 400 yd. Find the area of the field in acres. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Rectangle A = ℓw Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Parallelogram A = base x height = bh = ag Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Triangle Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Find the areas: 40 cm 2 4 cm 2 20 cm 2 Example 14-5 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Kite The area of a kite can be found by relating it to the area of a rectangle. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Trapezoid Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 14-6 Find the area of each trapezoid. 56 cm 2 15 cm 2 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Regular Polygon Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Circle Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Area of a Sector Copyright © 2013, 2010, and 2007, Pearson Education, Inc.