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. In this case the given prism is slanted, which means the height is measured on the outside. Examining the diagram, we can see that the height is one of the legs in a right triangle.
Note that the given side is the hypotenuse and the side we want to find is opposite to the given angle. Therefore, we will use the sine ratio.
sin θ = opposite/hypotenuse
In our triangle, we have that θ = 72^(∘), the hypotenuse is 18 m, and that the opposite side to θ is h. Let's substitute this information into the above formula, and solve for h.
We also see in the diagram that the base is a triangle and the lengths of the legs are 5, 13 and 12. Let's add them to find its perimeter.
P&= 5+ 13+ 12
P&=30m
Let's now substitute P = 30 and h= 17.1 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=513m^2. We can calculate the area of the base using the formula for area of a triangle.
The area of the base is 30m^2. Now we have enough information to find the surface area of the prism. Let's substitute 513 and 30 for L and B, respectively, into the corresponding formula.
