To find the surface area of a rectangular pyramid, we need to calculate the area of each of the five faces and then add them together.
The formula for the surface area of a rectangular pyramid is:
Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height
In this case, the base of the rectangular pyramid is a rectangle with dimensions 10 cm by 14 cm. The area of the base is:
Base Area = 10 cm * 14 cm = 140 cm^2
The slant height of the pyramid is the height of one of the triangle faces. We can find the slant height by using the Pythagorean theorem:
Slant Height = sqrt(10.6^2 + 12^2) = sqrt(112.36 + 144) = sqrt(256.36) = 16.01 cm
Now, we can calculate the surface area:
Surface Area = 140 cm^2 + (1/2) * (10 cm + 14 cm) * 16.01 cm = 140 cm^2 + 24.01 cm * 16.01 cm = 140 cm^2 + 384.2421 cm^2 = 524.2421 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 524.24 cm^2.
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