It is a triangular pyramid where each triangle has a base of 4 in and its faces measure 4 in, it has an inclined height of 6.646 in.
What is the surface area of Sally's pyramid? Write your answer in decimal form. Round to the nearest thousandth.
To find the surface area of the triangular pyramid, we need to find the area of each of the four triangles and the area of the base.
The area of each triangle is given by the formula:
Area = 1/2 * base * height
For each triangle:
Area = 1/2 * 4 * 6.646 = 13.292 square inches
Since there are four identical triangles, we can multiply the area of one triangle by 4 to get the total area of all four triangles:
4 * 13.292 = 53.168 square inches
Next, we need to find the area of the base triangle:
Area = 1/2 * base * height = 1/2 * 4 * 4 = 8 square inches
Finally, we add the areas of the four triangles and the base to get the total surface area of the pyramid:
Total Surface Area = 53.168 + 8 = 61.168 square inches
Therefore, Sally's pyramid has a surface area of 61.168 square inches.