what is the surface area of the rectangular pyramid 15 mm, 12 mm, 10 mm, 8 mm ??

Question

____, mm2

Answer 1

To find the surface area of a rectangular pyramid, we need to calculate the area of each of the five faces and 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

First, let's calculate the base area:
Base area = length * width = 15 mm * 12 mm = 180 mm^2

Next, let's calculate the perimeter of the base:
Perimeter of base = 2(length + width) = 2(15 mm + 12 mm) = 2(27 mm) = 54 mm

Now, let's calculate the slant height. To find the slant height, we will use the Pythagorean theorem:
slant height^2 = height^2 + (1/2 * perimeter of base)^2
slant height^2 = 10^2 + (1/2 * 54)^2
slant height^2 = 100 + (27)^2
slant height^2 = 100 + 729
slant height^2 = 829
slant height ≈ 28.8 mm

Finally, calculate the surface area:
Surface Area = base area + 1/2 * perimeter of base * slant height
Surface Area = 180 + 1/2 * 54 * 28.8
Surface Area = 180 + 777.6
Surface Area ≈ 957.6 mm^2

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