How much fabric is needed to make given the base does not need fabric ? A triangular pyramid without a base . The length base equilateral triangle is 15 inches , the height is 13 inches and height of the triangular faces is 18 inches
To find the amount of fabric needed to make the triangular pyramid, we first need to calculate the total surface area of the four triangular faces.
The formula to calculate the surface area of an equilateral triangle is
$$A = \frac{√3}{4} s^2$$
Where s is the length of the side of the equilateral triangle.
Given:
Height of the equilateral triangle (s) = 15 inches
Height of the triangular faces = 18 inches
Plugging the value of s into the formula, we get:
$$A = \frac{√3}{4} 15^2 = \frac{√3}{4} \times 225 = \frac{√3}{4} \times 225 = \frac{√3}{4} \times 225 = \frac{√3}{4} \times 225 = \frac{√3}{4} \times 225 = 97.43 sq. inches. $$
Now the total surface area of the four triangular faces is 4 times the area of one face.
So, the total surface area of the four triangular faces is:
$$97.43 \times 4 = 389.72 sq. inches$$
Therefore, the total amount of fabric needed to make the triangular pyramid without a base is 389.72 square inches.