find the area of a regular hexagon with the side length 4m. round to the nearest tenth
The area of a regular hexagon of side 4m is the same as that of 6 equilateral triangles with side 4m.
Area of an equilateral triangle
A=s²*√(3)/4
=4²*√(3)/4
=4√(3)
For the regular hexagon,
6A=24√(3)
To find the area of a regular hexagon, you can use the formula:
Area = (3√3 × side length^2) / 2
Given that the side length is 4m, let's substitute the value into the formula:
Area = (3√3 × 4^2) / 2
Area = (3√3 × 16) / 2
Area = (48√3) / 2
Area = 24√3
Now, let's round the result to the nearest tenth:
Area ≈ 24 × 1.732 ≈ 41.592
Rounded to the nearest tenth, the area of the regular hexagon is approximately 41.6 square meters.
To find the area of a regular hexagon, you can use the formula:
Area = (3√3 × s²) / 2
where "s" represents the length of one side of the hexagon.
In this case, the side length is given as 4m.
Substituting the value of "s" into the formula:
Area = (3√3 × 4²) / 2
Simplifying further:
Area = (3√3 × 16) / 2
Area = (48√3) / 2
Area = 24√3
Now, to round the area to the nearest tenth, you can use a calculator or compute the approximate value of √3, which is roughly 1.732.
Area ≈ 24 × 1.732
Area ≈ 41.568
Rounding the result to the nearest tenth:
Area ≈ 41.6 square meters
Therefore, the approximate area of a regular hexagon with a side length of 4m is 41.6 square meters.