We want to calculate the surface area of a triangular pyramid. Let's see the given measurements of the pyramid.
We can use a net to calculate the surface area of the pyramid. Let's see the net!
The net is made up of four triangles. We will calculate the area of each size of triangle separately, starting with the base. Let's substitute the measures of the base into the formula for the area of a triangle!
The area of the base is 35.1 square inches. Now let's take a look at the sides. Notice that the sides of the pyramid are congruent triangles. This means that they have the same area. Let's substitute the measures of the sides into the formula for the area of a triangle and simplify.
We found that the area of one side triangle is 31.5 square inches. Since the side triangles are congruent, the area of each of the side triangles is also 31.5 square inches. Now we have all the information that we need to find the total surface area of the triangular pyramid!
Total Surface Area
35.1+ 31.5+ 31.5+ 31.5=129.6in.^2
The total surface area of the triangular pyramid is 129.6 square inches.
