Let's recall the formula for the lateral area L of a prism.
L=Ph
Here, P is the perimeter of the base, and h the height of the prism. Note that the base is a right triangle. We see in the diagram that the lengths of the legs of this triangle are 8ft and 6ft. We can find the hypotenuse by using the Pythagorean Theorem.
Now we know the lengths of the three sides of the base. Let's add them to find its perimeter.
P&= 10+ 8+ 6
P&= 24ft
Let's now substitute P= 24 and h= 12 in the formula for the lateral area of a prism.
Let's recall the formula for the surface area of a prism.
S=L+2B
Here, L is the lateral area of the prism and B the area of the base. We already know that L=288ft^2. We can calculate the area of the base using the formula for area of a triangle.
The area of the base is 24ft^2. Now we have enough information to find the surface area of the prism. Let's substitute 288 and 24 for L and B, respectively, into the corresponding formula.
