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Honors Geometry Section 5.2 Areas of Triangles and Quadrilaterals

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You can see that the area of parallelogram ABCD is equal to the area of rectangle EBCF.

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For a parallelogram with base b and height h, the area is given by the formula: A parallelogram = ______ Note that the height is the length of the segment perpendicular to the base from a point on the opposite side which is called the altitude of the parallelogram.

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Any triangle is half of a parallelogram. For a triangle with base b and height h, the area is given by the formula: A triangle = ________ The height is the length of the ____________ to the base

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Example: Find the area of to the nearest 1000 th.

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Example: A triangle has an area of 56 and a base of 10. Find its height.

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Trigonometry and the Area of a Triangle Using your knowledge of trigonometry, express h in terms of sinC. Substituting this into the formula, and using a as the base we get

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We have just discovered that the area of a triangle can be expressed using the lengths of two sides and the sine of the included angle.

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Example: Use what you have learned above to find the area of parallelogram ABCD to the nearest 1000 th.

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An altitude of a trapezoid is a segment perpendicular to the two bases with an endpoint in each of the bases. The length of an altitude will be the height of the trapezoid.

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For a trapezoid with bases b 1 and b 2 and height h, the area of a trapezoid is given by the formula:

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Recall that the diagonals of both rhombuses and kites are perpendicular.

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