What is the surface area of the rectangular pyramid?
10 cm
14 cm
12 cm
10.6 cm
To calculate the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.
Given that the base is a rectangle with dimensions of 10 cm and 14 cm, the area of the base is:
Area = length x width = 10 cm x 14 cm = 140 cm^2
Next, we need to calculate the area of each triangular face. Since the pyramid is rectangular, the triangles are right triangles. The slant height (s) can be calculated using the Pythagorean theorem:
s = sqrt((10/2)^2 + 12^2)
s = sqrt(25 + 144)
s = sqrt(169)
s = 13 cm
Since there are 2 triangles with base 10 cm and height 13 cm and 2 triangles with base 14 cm and height 13 cm, the area of each triangular face is:
Area = 0.5 x base x height = 0.5 x 10 cm x 13 cm + 0.5 x 14 cm x 13 cm = 65 cm^2 + 91 cm^2 = 156 cm^2
Now, we can calculate 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 = Base Area + 4 x Triangle Area
Total Surface Area = 140 cm^2 + 4 x 156 cm^2
Total Surface Area = 140 cm^2 + 624 cm^2
Total Surface Area = 764 cm^2
Therefore, the surface area of the rectangular pyramid is 764 cm^2.