How much is needed to make a teepee triangular pyramid ? The slant height is 25 in , the base height is 26in and the base of the equilateral triangles is 30 inches
To calculate the total surface area of a triangular pyramid, you need to find the area of the three equilateral triangles that make up the sides of the pyramid and the area of the base triangle.
The formula for the area of an equilateral triangle is:
\[A = \frac{\sqrt{3}}{4} \times s^2\]
where s is the length of one side of the triangle.
Given that the base of the equilateral triangles is 30 inches, the area of one equilateral triangle would be:
\[A = \frac{\sqrt{3}}{4} \times 30^2 = \frac{\sqrt{3}}{4} \times 900 = 225\sqrt{3} \ in^2\]
Since there are three equilateral triangles making up the sides of the pyramid, the total area for the 3 sides will be:
\[3 \times 225\sqrt{3} = 675\sqrt{3}\ in^2\]
The base triangle of the pyramid can be calculated using the formula for the area of an equilateral triangle. Since the base height is given as 26 inches, the area of the base triangle is:
\[A = \frac{\sqrt{3}}{4} \times 26^2 = \frac{\sqrt{3}}{4} \times 676 = 169\sqrt{3} \ in^2\]
Now, to calculate the total surface area of the triangular pyramid, we sum the areas of the 3 sides and the base triangle:
\[Total \ area = 675\sqrt{3} + 169\sqrt{3} = 844\sqrt{3} \ in^2\]
Therefore, approximately 844√3 square inches of material is needed to create a triangular pyramid teepee.