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Honors Geometry Section 5.2 Areas of Triangles and Quadrilaterals

Honors Geometry Section 5.2 Areas of Triangles and Quadrilaterals. You can see that the area of parallelogram ABCD is equal to the area of rectangle EBCF. For a parallelogram with base b and height h , the area is given by the formula: A parallelogram = ______.

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Honors Geometry Section 5.2 Areas of Triangles and Quadrilaterals

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  1. Honors Geometry Section 5.2Areas of Triangles and Quadrilaterals

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

  3. 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.

  4. +

  5. 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

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

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

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

  9. 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.

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

  11. 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.

  12. For a trapezoid with bases b1 and b2 and height h, the area of a trapezoid is given by the formula:

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

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