To find the slant height of the triangular pyramid, we need to first calculate the lateral surface area of the pyramid.
The lateral surface area of a triangular pyramid can be calculated using the formula:
lateral surface area = 1/2 * perimeter of base * slant height
In this case, the lateral surface area is given as 78 in^2. Since the base of the pyramid is an equilateral triangle, the perimeter of the base can be calculated as 3 times the length of one side of the equilateral triangle.
To find the side length of the equilateral triangle, we use the formula for the area of an equilateral triangle:
Area = (√3 /4) * side^2
78 = (√3 /4) * side^2
78 = (√3 /4) * side^2
78 * 4/√3 = side^2
312/√3 = side^2
side = √(312/√3)
side ≈ 9.481
The perimeter of the base is 3 times the side length:
Perimeter = 3 * side
Perimeter = 3 * 9.481
Perimeter ≈ 28.44 in
Now we can plug in the values into the lateral surface area formula:
78 = 1/2 * 28.44 * slant height
78 = 14.22 * slant height
slant height = 78 / 14.22
slant height ≈ 5.476 in
Therefore, the slant height of the triangular pyramid is approximately 5.476 inches.
Use the net to find the slant height of the triangular pyramid made of equilateral triangles if its surface area is 78 in.2 .
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could i have a proper answer
Certainly! Here is the proper answer for finding the slant height of the triangular pyramid:
1. Given that the lateral surface area of the triangular pyramid is 78 in^2.
2. Because the base of the pyramid is made up of equilateral triangles, the lateral surface area can be calculated using the formula:
Lateral surface area = (1/2) * Base Perimeter * Slant Height
3. We know that the lateral surface area is 78 in^2.
4. The equilateral triangle's side length (s) can be found by first calculating the area of an equilateral triangle:
Area = (√3 / 4) * s^2
5. Equating the area to 78 in^2 and solving for s gives:
s = √(312/√3) ≈ 9.481 in
6. The base perimeter is 3 times the side length because it's an equilateral triangle.
Base Perimeter = 3 * 9.481 ≈ 28.44 in
7. Plug the values into the lateral surface area formula:
78 = (1/2) * 28.44 * Slant Height
Slant Height = 78 / 14.22 ≈ 5.476 in
So, the slant height of the triangular pyramid made of equilateral triangles with a surface area of 78 in^2 is approximately 5.476 inches.
1. Given that the lateral surface area of the triangular pyramid is 78 in^2.
2. Because the base of the pyramid is made up of equilateral triangles, the lateral surface area can be calculated using the formula:
Lateral surface area = (1/2) * Base Perimeter * Slant Height
3. We know that the lateral surface area is 78 in^2.
4. The equilateral triangle's side length (s) can be found by first calculating the area of an equilateral triangle:
Area = (√3 / 4) * s^2
5. Equating the area to 78 in^2 and solving for s gives:
s = √(312/√3) ≈ 9.481 in
6. The base perimeter is 3 times the side length because it's an equilateral triangle.
Base Perimeter = 3 * 9.481 ≈ 28.44 in
7. Plug the values into the lateral surface area formula:
78 = (1/2) * 28.44 * Slant Height
Slant Height = 78 / 14.22 ≈ 5.476 in
So, the slant height of the triangular pyramid made of equilateral triangles with a surface area of 78 in^2 is approximately 5.476 inches.
1 answer