find the area of the equilateral triangle if a side is 8 radical 3m. round to the nearest who number
tan 60° = height/4√3
height = (4√3)(√3)
= 12
area = (1/2)(8√3)(12) = 48√3
To find the area of an equilateral triangle, you can use the formula:
Area = (side^2 * √3) / 4
In this case, the length of one side is given as 8√3m.
Substituting the given values into the formula:
Area = (8√3^2 * √3) / 4
= (8 * 3 * 3 * √3) / 4
= (72√3) / 4
= 18√3
To round the answer to the nearest whole number, you can use the following guidelines:
- If the decimal part is 0.5 or above, round up to the next whole number.
- If the decimal part is less than 0.5, round down to the current whole number.
Since √3 is an irrational number (approximately 1.732), rounding it to the nearest whole number gives:
Area ≈ 18 * 1.732
≈ 31.176
Rounding 31.176 to the nearest whole number:
Area ≈ 31
Therefore, the area of the equilateral triangle is approximately 31 square meters.