Properties of a Triangular Pyramid

This is a triangular prism, which is a good example for introducing prisms and pyramids.
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A triangular pyramid features a triangle as its base, with three additional triangles extending from the edges of the base triangle. This differs from the square pyramid, which features a square as its base, with four triangles making up its sides. The properties of the triangular pyramid, such as its surface area and volume, can be calculated by using the values of the triangular length and height.

Slant Height

The triangular pyramid is composed of three slanted triangles extending from a base triangle, giving the triangular pyramid four surfaces. The slant height of the triangular pyramid is the length of a line extending from the tip of the pyramid to its base edge, forming a right angle with the edge. To determine the slant height of a triangular pyramid, square the length of one of the base triangle sides, then multiply this value by 1/12. The square root of this value plus the pyramid height squared is the slant height. Pyramids without an equilateral base are irregularly shaped, and feature unequal side lengths. Therefore, the slant height must be calculated individually for each side of the pyramid, using the same equation as previously stated.

Surface Area

The surface area is the total exterior area of the pyramid. The surface area of a regular triangular pyramid can be calculated by the slant height and perimeter values. To calculate the surface area this way, find the perimeter of the base triangle by adding together the length of its sides. Multiply this value by the pyramid slant height, then multiply that product by 1/2. To determine the surface area of an irregular pyramid, calculate the area of each triangle separately. To do so, multiply the triangle's base length by its slope height, then multiply the result by 1/2. Once the area of all four sides is known, add them together. The sum is the total surface area of the pyramid.

Volume

The volume is the total interior area of the pyramid. This can be calculated by the same equation used for other types of pyramids. To determine the volume of a triangular pyramid, multiply the area of the base triangle by true height of the pyramid, then multiply this value by 1/3. Note that the true height of the pyramid is the perpendicular length between the tip of the pyramid and the center of the base triangle, not the slant height.

Tetrahedron

A regular tetrahedron is a special case of the triangular pyramid. It is composed of four congruent, equilateral triangles. Therefore, when working with a tetrahedron, you can treat any of the triangles as the pyramid base when calculating its dimensions.

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