how do you find the volume and surface area of a regular triangular pyramid?
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a regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m³. Find the lateral areas of the pyramid.
84.65 m^2
To find the volume and surface area of a regular triangular pyramid, you will need to consider two main measurements: the slant height (l) and the base edge length (s).
The slant height is the distance from the center of the base to the apex, forming a slanted triangle with one of the triangular faces. The base edge length is the length of one side of the triangular base.
Here's how to calculate the volume and surface area of a regular triangular pyramid:
1. Volume:
The formula to calculate the volume of a pyramid is given by V = (1/3) * base area * height. In this case, since the base is a regular triangle, the formula becomes V = (√3/4) * s^2 * height.
To find the height (h), you can use the Pythagorean theorem:
h = √(l^2 - (s/2)^2).
2. Surface Area:
To calculate the surface area, add up the areas of all the triangular faces. For a regular triangular pyramid, it has four congruent triangular faces.
Area of one triangular face = (1/2) * base * height.
Since the base is an equilateral triangle, the formula becomes A = (1/2) * s * height.
Therefore, the total surface area of a regular triangular pyramid is A = 4 * (1/2) * s * height.
By using these formulas, you can find the volume and surface area of a regular triangular pyramid with known slant height (l) and base edge length (s).