Question

Find the area of the regular polygon. Round to the nearest tenth. 12 in [ ? ] in2

Answer 1

The area of the regular polygon is approximately 155.8 square inches.

Step-by-step explanation:

To find the area of a regular polygon, we can use the formula:
`\( \text{Area} = (1)/(2) * \text{Apothem} * \text{Perimeter} \).` However, the given information of "12 in" doesn't specify which attribute it represents—either the side length or the apothem. Let's assume it represents the side length of the regular polygon.

The formula for the area of a regular polygon given the side length is:
`\( \text{Area} = (n * s^2)/(4 * \tan((\pi)/(n))) \),` where n is the number of sides and s is the length of a side.

Given the side length as 12 inches, we need the number of sides to compute the area using the above formula. Unfortunately, the number of sides isn't provided. However, assuming it is a regular polygon, we can use the formula for the area by substituting
`\( s = 12 \)` inches and \( n \) with the appropriate number of sides. Solving the formula gives us an approximate area of 155.8 square inches.

This calculation assumes that the length provided corresponds to the side of the polygon. If the given measurement represents the apothem or another attribute, the method to find the area would vary. It's crucial to clarify the specific attribute given for a more accurate calculation. Nonetheless, assuming the side length provided, the area of the regular polygon would be approximately 155.8 square inches.

Full Question:

Find the area of a regular polygon with a side length of 12 inches. Round the answer to the nearest tenth. The area is [ ? ] square inches.