Find the area of the pentagon four inches sixteen inches six inches nine inches
To find the area of a pentagon, we need to know both the side length and the apothem (the segment from the center of the pentagon to the midpoint of one of its sides). Since we're only given the side lengths, we'll use the formula for the area of a regular pentagon:
Area = (5 × s²)/(4 × tan(π/5))
where s is the side length.
Given that the side length is 6 inches, we can calculate the area:
Area = (5 × 6²)/(4 × tan(π/5))
Area = (5 × 36)/(4 × 0.726542528)= 90/2.906170769
Area ≈ 30.955 square inches
Therefore, the area of the pentagon is approximately 30.955 square inches.