A pyramid composed of four equilateral triangles, called a tetrahedron, has a one-side length of 5 meters. What is its surface area? Round the answer to the nearest tenth.
43.3
To find the surface area of a tetrahedron, we first need to determine the area of each of its faces. Since the tetrahedron is composed of equilateral triangles, the formula for calculating the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side^2
Given that the side length of each triangle is 5 meters, we can substitute this value into the formula:
Area = (sqrt(3) / 4) * 5^2
Area = (sqrt(3) / 4) * 25
Area = (1.732 / 4) * 25
Area = 4.33 * 25
Area = 108.25 square meters
Since there are four triangular faces on the tetrahedron, we multiply the area of one triangle by 4:
Surface Area = 108.25 * 4
Surface Area = 433 square meters
Therefore, the surface area of the tetrahedron is approximately 433 square meters.
To find the surface area of a tetrahedron, we need to calculate the area of each of its four equilateral triangles.
The formula for the area of an equilateral triangle is given by:
Area = (√3/4) * side^2 ,
where "side" represents the length of one side of the equilateral triangle.
In this case, the length of one side of the tetrahedron is given as 5 meters. So, we can substitute this value into the formula:
Area = (√3/4) * 5^2 .
Now, let's calculate the area of one triangle using this formula:
Area = (√3/4) * 25
= (√3 * 25) / 4
= (5√3) / 4.
Since the tetrahedron is composed of four equilateral triangles, we need to multiply the area of one triangle by 4 to get the total surface area of the tetrahedron.
Total Surface Area = 4 * (5√3) / 4
= 5√3.
Now, let's calculate the numerical value:
Total Surface Area ≈ 8.7 (rounded to the nearest tenth).
Hence, the surface area of the tetrahedron is approximately 8.7 square meters.