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27 July, 22:02

A pentegon can be divided into five congruent triangles as shown. the function y=5 tan theta models the height of each triangle. what is the area of the pentagon if theta=54 degrees?

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  1. 27 July, 22:19
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    We are required to calculate the area of the pentagon whose height is given by y=5 tan theta

    where; theta=54°

    but

    tan theta=[opposite]/[adjacent]

    thus

    opposite=adjacent tan theta

    since

    5tan54=opposite

    adjacent=5

    Therefore the base of the pentagon will be

    (5+5) = 10

    Area of a triangle is given by:

    A=1/2 (base*height) sin theta

    The area of one triangle forming the pentagon will be:

    A=1/2 * (10*5tan54) * sin54

    A=27.84 square units

    Thus the area of pentagon will be:

    Area = (# triangles) * (area of one triangle)

    =27.84*5

    =139.2 square units
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