find the surface area of a rectangular pyramid with these measurements: I = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth
___ m^2
To find the surface area of the rectangular pyramid, we need to find the area of each face and then add them up.
The base of the pyramid is a rectangle with dimensions I = 15 m and w = 12 m. So, the area of the base is A = I * w = 15 * 12 = 180 m².
To find the area of the other faces, we need to find the area of each triangular face. The height of each triangular face is h = 10 m, and the length of each base edge is the same as the corresponding dimension of the rectangle.
To find the area of each triangular face, we can use the formula for the area of a triangle:
A_triangle = 1/2 * base * height
The base of each triangular face is the same as the length of the corresponding dimension of the rectangle. So, the length of the base for each triangular face is I = 15 m.
Plugging in the values, we have:
A_triangle = 1/2 * 15 * 10 = 75 m²
Since we have 4 triangular faces, we need to multiply this area by 4:
A_triangular_faces = 4 * 75 = 300 m²
Finally, the surface area of the rectangular pyramid is the sum of the area of the base and the area of the triangular faces:
A_pyramid = A_base + A_triangular_faces = 180 + 300 = 480 m²
Therefore, the surface area of the rectangular pyramid is 480 m².