The given solid is a triangular prismnot a cone. To calculate the surface area of a prism, we can use the known formula where P is the perimeter of the base, h is the height, and B is the area of the base.
S=Ph+2B
Since the base of the given triangular prism is an equilateral triangle, we know that all its sides are congruent and its interior angles have a measure of 60^(∘). Therefore, let's add them to find the perimeter of the base.
P=8+8+8= 24cm
The area of a triangle is half the product of its side and its height. We are given the side but we are missing the height.
Note that the height bisects both the vertex angle of the triangle and the opposite side of the vertex, which is a side of the equilateral triangle. As a result, a 30^(∘)-60^(∘)-90^(∘) triangle is created. The length of its shorter leg is 8÷ 2=4cm.
In this type of special triangle the length of the longer leg, which is also the height of the larger triangle, is sqrt(3) times the length of the shorter leg.
Longer Leg: sqrt(3)* 4= 4sqrt(3)cm
Therefore, the height is 4sqrt(3)cm.
Let's substitute the found segments lengths into the formula for the area of a triangle and simplify.
The area of the base is about 27.7cm^2. Now we have enough information to find the surface area of the prism. Let's substitute P with 24, h with 3, and B with 27.7 into the formula.
