Use the image to answer the question. What is the surface area of the rectangular pyramid? the lengths are 10 c 10.6c 14c and 12c

Answer 1

To find the surface area of a rectangular pyramid, you need to calculate the area of the two triangles (base and side) and the area of the three rectangles (three faces).

First, calculate the area of the base triangle:
Area_base = (1/2) * base_length * height
Area_base = (1/2) * 14c * 12c
Area_base = 84c^2

Next, calculate the area of the side triangle (use Pythagorean theorem to find the slant height):
slant_height = sqrt((10.6c)^2 + (12c)^2)
slant_height = sqrt(112.36c^2 + 144c^2)
slant_height = sqrt(256.36c^2)
slant_height ≈ 16c

Area_side = (1/2) * base_length * slant_height
Area_side = (1/2) * 10.6c * 16c
Area_side ≈ 84.8c^2

Now, calculate the area of the three rectangles:
Area_rectangles = 2 * (10c * 10.6c + 10.6c * 14c + 10c * 14c)
Area_rectangles = 2 * (106c^2 + 148.4c^2 + 140c^2)
Area_rectangles = 2 * 394.4c^2
Area_rectangles = 788.8c^2

Finally, sum up all the areas to get the total surface area of the rectangular pyramid:
Surface Area = Area_base + Area_side + Area_rectangles
Surface Area = 84c^2 + 84.8c^2 + 788.8c^2
Surface Area = 957.6c^2

Therefore, the surface area of the rectangular pyramid is 957.6c^2.