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
We can see that the base is a right triangle. We are given the lengths of both legs, but not the length of the hypotenuse. Let's use the Pythagorean Theorem to find the length of the hypotenuse.
hypothenuse = sqrt(3^2 + 4^2) ⇔ hypothenuse = 5
Let's add the lengths of the three sides of the triangle to find the perimeter.
P=3+4+5=12cm
We can calculate the area of the base using the formula for the area of a triangle.
The area of the base is 6cm^2. Now we have enough information to find the surface area of the prism. Let's substitute P with 12, h with 2, and B with 6 into the formula.
