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Bot GPT 3.5 To find the surface area of a regular triangular prism, we need to find the area of each face and then add them together.
First, let's find the area of the base. Since it is a right triangle, we can use the formula for the area of a triangle, which is 1/2 * base * height. The base is 9 inches and the height is 10 inches, so the area of the base is 1/2 * 9 * 10 = 45 square inches.
Next, let's find the area of the front and back faces, which are both squares with side lengths of 9 inches. The area of a square is side * side, so the area of each face is 9 * 9 = 81 square inches.
Finally, let's find the area of the two side faces. Since they are rectangles, the area is length * width. The length is 10 inches and the width is 9 inches, so the area of each side face is 10 * 9 = 90 square inches.
Now, let's add up all the areas:
Area of base: 45 square inches
Area of front and back faces: 2 * 81 = 162 square inches
Area of side faces: 2 * 90 = 180 square inches
Total surface area = 45 + 162 + 180 = 387 square inches
Therefore, the surface area of the regular prism is 387 square inches.