Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards long. Round your answer to the nearest tenth.
Can someone please help me with this??
area = 1/2 x perimeter x apothem
it's 6 isosceles triangles ... base = 13 ... height = 11.4
Yes, I can help you with that! Here's a step-by-step solution to find the area of a regular hexagon with the given measurements:
Step 1: Calculate the length of a regular hexagon's radius.
Since the apothem and the side length are given, we can use the formula:
radius = apothem + side length
radius = 11.4 yards + 13 yards
radius = 24.4 yards
Step 2: Calculate the area of a regular hexagon using the formula.
The formula for the area of a regular hexagon is:
area = (3√3 * side length^2) / 2
Plugging in the given side length:
area = (3√3 * 13^2) / 2
area = (3√3 * 169) / 2
area ≈ 439.5 square yards
Rounding the answer to the nearest tenth, the area of the regular hexagon is approximately 439.5 square yards.
I hope this helps! Let me know if you have any further questions.
Certainly! To find the area of a regular hexagon, you can use the formula:
Area = (3√3 / 2) * s^2
where "s" represents the length of one side of the hexagon.
In this case, the length of one side of the hexagon is given as 13 yards. Let's substitute the values into the formula:
Area = (3√3 / 2) * 13^2
Calculating the value of 13^2, we get:
Area = (3√3 / 2) * 169
Now, let's calculate the value of (3√3 / 2):
(3√3 / 2) ≈ 2.598
Now substitute this back into the formula:
Area ≈ 2.598 * 169
Calculating the product, we get:
Area ≈ 439.762
Since we need to round the answer to the nearest tenth, the area of the regular hexagon with an apothem of 11.4 yards and a side length of 13 yards is approximately 439.8 square yards.