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# Class Note for MATH 1330 with Professor Flagg at UH

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This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15
Math 1330 Section 72 Area Area of a Triangle Given any triangle not necessarily a right triangle where we know the length of two of the sides and the measure of the acute angle in between them we can calculate the area of the triangle by the following formula A ab sint9 A I b Note that asin0 is equal to the height of the triangle So the formula is a simple application of the area of a triangle formula area equals onehalf base times height The formula is valid even if the angle is not acute Example 1 Find the area ofa triangle with sides oflength 4 cm and 6 cm and a 45 degree angle between these two sides Area of a Segment ofa Circle A The sector of the circle is the wedge intercepted by angle theta It consists of two pieces triangle ABC and the segment bounded by the chord AB and the arc of the circle intercepted by this chord The area of triangle ABC is Area r2 sint9 The area ofthe sector intercepted by angle 6 is Area r20 So the area ofthe segment is Area segment 12 12 rt9 r s1nt9 2 2 Example 2 Find the area ofa segment ofa circle of radius 4 cm made from a 60 degree angle Area of a Regular Polygon We can use these area formulas to nd the area of a regular polygon inscribed in a circle of radius r A regular ngon is a gure with 11 equal sides and 11 equal angles Square 7 four sides Pentagon 7 ve sides Hexagon 7 six sides Octagon 7 eight sides Nonagon 7 nine sides Decagon 7ten sides Dodecahedron 7twelve sides Example 3 Find the area of the regular hexagon inscribed in a circle of radius 12 cm Example 4 Find the area of a regular octagon with sides of length 8 cm

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