If X = 8 units, Y = 12 units, Z = 15 units, and h = 5 units, what is the surface area of the triangular prism shown above? A. 420 square units B. 450 square units C. 480 square units D. 540 square units
To find the surface area of the triangular prism, we need to first calculate the surface area of both triangular bases and the three rectangular sides.
1. The surface area of one triangular base is given by the formula:
A = (1/2) * base * height
A = (1/2) * 8 * 5
A = 20 square units
Since there are two triangular bases, the total surface area of the bases is:
20 * 2 = 40 square units
2. The surface area of the three rectangular sides can be calculated by finding the area of each rectangle and adding them together.
The area of the rectangle with sides X and Y is:
8 * 12 = 96 square units
The area of the rectangle with sides X and Z is:
8 * 15 = 120 square units
The area of the rectangle with sides Y and h is:
12 * 5 = 60 square units
Therefore, the total surface area of the three rectangular sides is:
96 + 120 + 60 = 276 square units
Adding the surface area of the bases to the surface area of the three rectangular sides:
40 + 276 = 316 square units
Thus, the correct answer is not included in the options provided.