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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 5.2Areas 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 = ______ 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.
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
Example: A triangle has an area of 56 and a base of 10. Find its height.
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
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.
Example: Use what you have learned above to find the area of parallelogram ABCD to the nearest 1000th.
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.
For a trapezoid with bases b1 and b2 and height h, the area of a trapezoid is given by the formula:
Recall that the diagonals of both rhombuses and kites are perpendicular.