"Published in Vacaville, California, USA"
The plane area shown in the figure consists of an isosceles trapezoid (non-parallel sides equal) and a segment of a circle. If the non-parallel sides are tangent to the segment at points A and B, find the area of the composite figure.
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| Photo by Math Principles in Everyday Life |
Solution:
The given plane figure consists of an isosceles trapezoid and a circular segment. Let's analyze and label further the above figure as follows
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| Photo by Math Principles in Everyday Life |
From point A, draw a line perpendicular to CA and from point B, draw a line perpendicular to BD. The intersection of the two lines is point O which is the center of a circular arc. By using the laws of angles, ∆AOB is an isosceles triangle because the two base angles and their opposite sides are equal. If ∆AOB is an isosceles triangle, then the altitude h bisects AB into two equal parts which are 1.5'' each.
The angle of a circular arc is
Hence, the area of a circular segment is
The height of a circular segment is
The length of the upper base of a trapezoid is
Then the above equation becomes
Hence, the area of a trapezoid is
Therefore, the area of a plane figure is
