The figure below is a net for a rectangular prism. Side a = 70 centimeters, side b = 21 centimeters, and side c = 29 centimeters. What is the surface area of this figure?
To find the surface area of the rectangular prism, we need to find the area of each of the six faces and then add them up.
Face 1: The front face is a rectangle with sides a = 70 cm and b = 21 cm. The area of this face is ab = 70 cm x 21 cm = 1470 cm^2.
Face 2: The back face is also a rectangle with the same dimensions as the front face. So, its area is also 1470 cm^2.
Face 3: The top face is a rectangle with sides a = 70 cm and c = 29 cm. The area of this face is ac = 70 cm x 29 cm = 2030 cm^2.
Face 4: The bottom face is also a rectangle with the same dimensions as the top face. So, its area is also 2030 cm^2.
Face 5: The left face is a rectangle with sides b = 21 cm and c = 29 cm. The area of this face is bc = 21 cm x 29 cm = 609 cm^2.
Face 6: The right face is also a rectangle with the same dimensions as the left face. So, its area is also 609 cm^2.
Now, we can add up the areas of all six faces to get the surface area:
Surface area = Face 1 + Face 2 + Face 3 + Face 4 + Face 5 + Face 6
Surface area = 1470 cm^2 + 1470 cm^2 + 2030 cm^2 + 2030 cm^2 + 609 cm^2 + 609 cm^2
Surface area = 9218 cm^2
Therefore, the surface area of the rectangular prism is 9218 cm^2.