Use the net to find the slant height of the triangle pyramid made of an equilateral triangles if its surface area is 78 in.²
To find the slant height of the triangular pyramid, we first need to find the height of the pyramid.
Given that the surface area of the pyramid is 78 in², we can use the formula for the surface area of a pyramid, which is given by:
Surface Area = 0.5 * Perimeter of base * Slant height + Area of base
Since the base of the pyramid is an equilateral triangle, we can calculate the perimeter and area of the base.
An equilateral triangle has three equal sides, so the perimeter of the base can be calculated as:
Perimeter = 3 * side length
Let's assume the side length of the equilateral triangle is 's'.
Perimeter = 3s
Since the surface area of the pyramid is given as 78 in², we can say:
0.5 * 3s * Slant height + (sqrt(3)/4)*s² = 78
Simplifying the equation, we can express the slant height in terms of 's' as:
Slant height = (78 - (sqrt(3)/4)*s²) / (1.5s)
Therefore, the slant height of the triangular pyramid would be given by the formula above once the value of 's' is known.