Question
If the surface area of a rectangular pyramid was 1,178.8 cm squared what would the measurements of the pyramid be
Answers
GPT 3.5
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.
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.