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Published byErnest Cross Modified over 9 years ago
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11.3 The Area Of A Trapezoid Objective: After studying this section you will be able to find the areas of trapezoids and us the measure of a trapezoid’s median to find its area
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The Area of a Trapezoid You saw in the last lesson that we can divide a trapezoid into simpler shapes. b2b2 b1b1 h There is a formula though to make finding the area easier.
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TheoremThe area of a trapezoid equals one-half the product of the height and the sum of the bases. where b 1 is the length of one base, and b 2 is the length of the other base, and h is the height.
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The Median of a Trapezoid DefinitionThe line segment joining the midpoints of the non-parallel sides of a trapezoid is called the median of the trapezoid. median
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TheoremThe measure of the median of a trapezoid equals the average of the measures of the bases. where b 1 is the length of one base and b 2 is the length of the other base.
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TheoremThe area of a trapezoid is the product of the median and the height. where M is the length of the median and h is the height. If we know the median then we can use a shorter formula to find the area of a trapezoid.
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Example 1 Find the area of the trapezoid 12 cm 18 cm Example 2 7 cm Find the shorter base of the trapezoid if the area is 52, its altitude is 8, and its longer base is 10. (Hint: draw a picture)
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Example 3 Find the median of a trapezoid with height 12 and bases 6 and 14. (Hint: draw a picture) Example 4 Find the area of the trapezoid in example 3.
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Summary State in your own words how you can find the area of a trapezoid. Homework: worksheet
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