To find the area of a regular hexagon given a radius (or circumradius) of 5 inches, you can use the formula:
Area = (3√3/2) × r²,
where r is the radius.
Step 1: First, square the radius:
r² = 5² = 25.
Step 2: Multiply the squared radius by (3√3/2):
Area = (3√3/2) × 25.
To calculate (3√3/2):
– Calculate √3, which is approximately 1.732.
– Then multiply this by 3: 3 × 1.732 = 5.196.
– Now divide by 2: 5.196 / 2 = 2.598.
Step 3: Multiply this value by 25:
Area = 2.598 × 25 = 64.95.
Final Answer: The area of the regular hexagon is approximately 64.95 square inches.