Use the image to answer the question.
An illustration shows a triangular pyramid with an equilateral base. The perpendicular height of the base measures 12 inches and all sides measure 14 inches. The slant height measures 13 inches.
Use nets to find the surface area of the triangular pyramid with an equilateral base.
(1 point)
Responses
84 in.2
84 in. squared
273 in.2
273 in. squared
357 in.2
357 in. squared
175 in.2
To find the surface area of the triangular pyramid with an equilateral base, we need to find the area of each face and then add them together.
Given that all sides measure 14 inches, the base of the pyramid is an equilateral triangle with side length 14 inches. The area of an equilateral triangle can be found using the formula:
Area = (sqrt(3)/4) * side^2
Area = (sqrt(3)/4) * 14^2
Area = (sqrt(3)/4) * 196
Area = 49sqrt(3)
So, the area of each triangular face is 49sqrt(3) square inches.
Now, we need to find the area of the three triangular faces:
Area = 3 * 49sqrt(3)
Area = 147sqrt(3)
Given that the slant height is 13 inches, we can find the area of the triangular face by using the formula:
Area = base * slant height / 2
Area = 14 * 13 / 2
Area = 91 square inches
Finally, the total surface area of the pyramid is the sum of the areas of the triangular faces:
Total Surface Area = 147sqrt(3) + 91
Total Surface Area = 273 in. squared
Therefore, the surface area of the triangular pyramid with an equilateral base is 273 in. squared.