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An illustration shows the net of a triangular prism. The illustration forms a shape where the small triangle is in the middle with each side being the base of three different triangles. The height of the triangle in the middle is 5 inches as shown by a dashed line and the base is 6 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 .
(1 point)
First, we need to find the lateral surface area of the triangular pyramid. The lateral surface area of a pyramid is given by the formula:
Lateral Surface Area = 1/2 * base perimeter * slant height
Since the base of the triangular pyramid is an equilateral triangle with sides of 6 inches, the base perimeter is 3 * 6 = 18 inches.
Given that the lateral surface area is 78 in^2, we can set up the equation:
78 = 1/2 * 18 * slant height
78 = 9 * slant height
slant height = 78 / 9
slant height ≈ 8.67 inches
Therefore, the slant height of the triangular pyramid made of equilateral triangles is approximately 8.67 inches.