The area of the polygon is 83 sq.inch , Option D is the answer.
The missing figure is attached with the answer.
A closed figure with three or more sides is a polygon , A triangle , quadrilateral ,pentagon, etc are all polygon.
It is given that
Area of the polygon needs to be determined
The polygon is a pentagon
Side of rectangle is 8 inches * 5 inches
and two triangles with heights of 7 inches and 6 inches.
From the figure , to calculate the total area
Total Area of polygon = Area of the rectangle + area of triangle 1 + area of triangle 2
Area of rectangle = length * Breadth
Area of Rectangle = 8*5 = 40 sq.inch
Area of triangle 1 = (1/2) * base * height
Area of triangle 1 = (1/2) * 8 *7
Area of triangle 1 = 28 sq.inch
Area of Triangle 2 = (1/2) * 5* 6
Area of Triangle 2 = 15 sq.inch
Total Area = 40 + 28+15
Total Area = 83 sq.inch
Therefore the area of the polygon is 83 sq.inch , Option D is the answer.
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