As you can see in the diagram, the triangular prism has the following faces:
1) Two triangular faces
2) Three rectangular faces.
Surface area is the SUM of the areas of all of the faces.
Let us find these faces one by one:
1.
As you know, the area of the triangle is:
[tex] \frac{1}{2} * base * height [/tex]
Since, the base = 6 inches, and height = 4 inches;
Therefore, The area of ONE triangle = (1/2) * 6 * 4 = 12 inches squared.
In triangular prism, there are two triangles, therefore,
Two triangular faces = 2 * 12 inches = 24 inches squared --- (A)
2.
Now let us find the areas of three rectangular faces...
Since, two of the three rectangular faces are the same, therefore, we would find the area of one rectangular face, and multiple the result with two to get the total area of two rectangular faces.
Area of one rectangular face = base * height.
Since, base = 0.5 inches, height = 5 inches, therefore,
Area of one rectangular face = 0.5 * 5 = 2.5 inches squared.
Now that we have one rectangular face, therefore,
Area of two rectangular faces = 2 * 2.5 = 5 inches squared.
The area of the third rectangular base = 6 * 0.5 = 3 inches squared
Therefore,
The area of the three rectangular faces = 5 + 3 = 8 inches squared --- (B)
Now add both "area of two triangular faces(A)" and "area of three rectangular faces(B)" to get the final surface area of the triangular prism.
Surface Area of the triangular prism = Area of Two Triangular faces + Area of Three Rectangular faces
Surface Area = 24 + 8 = 32 inches squared
The surface area of the triangular prism = 32 inches squared.
The correct option is: d
-i
