Answer :
Final answer:
The area of a pentagon with a perimeter of 45cm is calculated by first finding the length of one side (9cm) and then substituting this into the formula for the area of a pentagon. The final area is 31.21 cm².
Explanation:
To solve for the area of a regular pentagon, we first need to determine the length of one side. Since the perimeter of a pentagon is the sum of the lengths of all its sides and we are told that the perimeter is 45cm, we divide this by 5 (the number of sides in a pentagon) to find each side is 9cm.
Next, we use the formula for the area of a regular pentagon:
Area = (1/4) * √(5 * (5 + 2*√(5))) * side².
When we substitute our side value into the formula, it is as follows:
Area = (1/4) * √(5 * (5 + 2*√(5))) * (9²)
= 31.21 cm².
This method can be used to determine the area of a regular pentagon if you only know its perimeter.
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