A triangular prism is a prism that has triangular bases. Let's take a look at the given diagram.
The surface area of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces. Let's calculate the area of the triangular bases and the area of the rectangular faces one at a time. Then we can add them together.
Triangular Bases
The triangular bases of the given prism are right triangles with legs that are 12 feet and 9 feet long. In right triangles, the legs are perpendicular, so each of the legs is also a height falling onto the other leg. Therefore, the area of a right triangle is half the product of the legs. Let's use this fact to find the area of one of the prism's bases.
B = 1/2( 12)( 9) = 54
The area of one triangular base is 54 square feet. Because both of the triangular bases are exactly the same, we know that the area of the second triangular base is 54 square feet as well. Let's add them together!
Area of the Triangular Bases
54+54= 108ft^2
Rectangular Faces
Now, let's focus on the areas of the rectangular faces.
We can see that all three rectangular faces have a width of 10 feet. Also, their lengths are 12, 9, and 15 feet. Let's substitute the length and the width of each rectangle in the formula for the area of a rectangle to obtain their areas.
A=l w
Measures
Substitute
Evaluate
l= 12, w= 10
A= 12( 10)
A= 120ft^2
l= 9, w= 10
A= 9( 10)
A= 90ft^2
l= 15, w= 10
A= 15( 10)
A= 150ft^2
Surface Area of the Prism
Finally, to get the surface area of the triangular prism, we add the area of both triangular bases and the area of the three rectangular faces.
Surface Area of the Triangular Prism
108+ 120+ 90+ 150=468ft^2
Therefore, answer D is correct.
