Find the area of a regular pentagon with side equal to 3 and apothem equal to K.
To find the area of a regular pentagon, you can use the formula:
Area = (Perimeter * Apothem) / 2
In this case, you know the side length of the pentagon is 3, and the apothem is represented by K. Let's calculate the perimeter of the pentagon first.
Since the pentagon is regular, all sides are equal. Therefore, the perimeter of the pentagon is:
Perimeter = 5 * side length
= 5 * 3
= 15
Now that we have the perimeter and the apothem, we can substitute these values into the area formula:
Area = (Perimeter * Apothem) / 2
= (15 * K) / 2
= (15K) / 2
= 7.5K
Hence, the area of the given regular pentagon with a side length of 3 and an apothem of K is 7.5K.