If the surface area of a rectangular pyramid was 1,178.8 cm squared what would the measurements of the pyramid be

Answer 1

To find the measurements of the rectangular pyramid, we need to first determine the length, width, and height of the pyramid.

The surface area formula for a rectangular pyramid is:

Surface Area = 2lw + lh + wh

Where l is the length, w is the width, and h is the height of the pyramid.

Given that the surface area is 1,178.8 cm squared, we can set up the equation:

1,178.8 = 2lw + lh + wh

Since we do not have any specific dimensions, we need to work with variables. Let's assume that the length = 2x, width = 3x, and height = 4x.

Substitute these values into the equation:

1,178.8 = 2(2x)(3x) + 2(2x)(4x) + 3x(4x)
1,178.8 = 24x^2 + 16x^2 + 12x^2
1,178.8 = 52x^2

Divide by 52:
x^2 = 22.65

Now find the values of x:
x = sqrt(22.65)
x ≈ 4.76

Therefore, the length is approximately 2(4.76) = 9.52 cm, the width is approximately 3(4.76) = 14.28 cm, and the height is approximately 4(4.76) = 19.04 cm.

The dimensions of the rectangular pyramid are approximately 9.52 cm x 14.28 cm x 19.04 cm.