Final Answer-Explanation:
To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the four triangular faces and then sum them all together.
First, we calculate the area of the base which is a rectangle:
Area of the base = length width
Area of the base = 15m 12m
Area of the base = 180 square meters
Next, let's calculate the area of the four triangular faces:
We use the formula for the surface area of a triangular face of a pyramid:
Area of a triangular face = (1/2) base length height
We have two triangles with base length = 15m and height = 10m and two triangles with base length = 12m and height = 10m.
Area of one triangular face with base length = 15m:
Area = (1/2) 15m 10m
Area = 75 square meters
Area of one triangular face with base length = 12m:
Area = (1/2) 12m 10m
Area = 60 square meters
There are two of each of these triangular faces, so the total area for all four of them is:
Total area for all four triangular faces = 2 (75m^2) + 2 (60m^2)
Total area for all four triangular faces = 150m^2 + 120m^2
Total area for all four triangular faces = 270 square meters
Now we can find the total surface area of the rectangular pyramid by summing the area of the base and the area of the four triangular faces:
Total surface area = Area of the base + Total area for all four triangular faces
Total surface area = 180m^2 + 270m^2
Total surface area = 450 square meters
So, the surface area of the rectangular pyramid with dimensions l = 15m, w = 12m, and h = 10m is 450 square meters.
