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 length of one leg of this triangle is 9cm and the length of the hypotenuse is 20cm. We can find the length of the missing leg 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&= 17.9+ 9+ 20
P&= 46.9cm
We will now substitute P= 46.9 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=562.8cm^2. We can calculate the area of the base using the formula for area of a triangle.
The area of the base is 80.55cm^2. Now we have enough information to find the surface area of the prism. Let's substitute 562.8 and 80.55 for L and B, respectively, into the corresponding formula.
