Calculate the area of the regular polygon below. The distance from the base to the center of the polygon is marked.View Image DescriptionA regular pentagon on a coordinate plane with the following attributes:A dashed line connects a center point G to base AB. The line is labeled 9.63.The vertices A and B are plotted at (0, 0) and (14, 0) respectively.463.68 units squared672 units squared337.05 units squared448 units squared
Question
Calculate the area of the regular polygon below. The distance from the base to the center of the polygon is marked.View Image DescriptionA regular pentagon on a coordinate plane with the following attributes:A dashed line connects a center point G to base AB. The line is labeled 9.63.The vertices A and B are plotted at (0, 0) and (14, 0) respectively.463.68 units squared672 units squared337.05 units squared448 units squared
Solution
To calculate the area of a regular polygon, you can use the formula:
Area = 1/2 * Perimeter * Apothem
The apothem is the distance from the center of the polygon to the midpoint of any side, which is given as 9.63 units.
The perimeter of a regular pentagon (5-sided polygon) can be calculated by multiplying the length of one side by the number of sides. The length of one side (AB) is given as the distance between the points (0,0) and (14,0), which is 14 units. So, the perimeter is 5 * 14 = 70 units.
Substituting these values into the formula gives:
Area = 1/2 * 70 * 9.63 = 337.05 units squared
So, the area of the regular pentagon is 337.05 units squared.
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