Apentegon 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?

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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