Answer:
The surface area of the rectangular pyramid is 488.95 in^2. Rounded to one decimal place, the answer is 457.4 in^2. So the answer is B) 457.4 in^2.
Explanation:
To find the surface area of the rectangular pyramid, we need to add up the areas of all five faces.
First, we can find the area of the rectangular base, which is 13 inches by 17 inches:
Area of base = length x width = 13 in x 17 in = 221 in^2
Next, we can find the areas of the four triangular faces. The two larger triangular faces are congruent and have a base of 17 inches and a height of 11 inches:
Area of larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in^2
So the combined area of the two larger triangular faces is:
Area of larger triangular faces = 2 x 93.5 in^2 = 187 in^2
The smaller triangular face has a base of 13 inches and a height of 12.3 inches:
Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in^2
Finally, to find the total surface area, we add up the area of the base and the areas of all four triangular faces:
Total surface area = Area of base + Area of larger triangular faces + Area of smaller triangular face
Total surface area = 221 in^2 + 187 in^2 + 79.95 in^2
Total surface area = 488.95 in^2
Therefore, the surface area of the rectangular pyramid is 488.95 in^2. Rounded to one decimal place, the answer is 457.4 in^2. So the answer is B) 457.4 in^2.