To find the length of the pyramid, we need to calculate the length of the slant height. The slant height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
In this case, the slant height (9 meters) is the hypotenuse, the perpendicular height (8.8 meters) is one of the sides, and the distance from the center of the base to the edge of the base (half of the length of the base, which is 3 meters) is the other side.
Therefore, we can calculate the length of the slant height as follows:
Slant height^2 = Perpendicular height^2 + Base half-width^2
Slant height^2 = 8.8^2 + 3^2
Slant height^2 = 77.44 + 9
Slant height^2 = 86.44
Slant height = √86.44
Slant height ≈ 9.30 meters
Since the length of the pyramid is equal to twice the slant height (as it is a rectangular pyramid), the length of the pyramid is:
Length of pyramid = 2 x Slant height
Length of pyramid = 2 x 9.30
Length of pyramid = 18.60 meters
Therefore, the length of the pyramid is approximately 18.60 meters.
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base of length 6 meters and width 2 meters. The perpendicular height from the apex to the center of the base is labeled 8.8 meters. The slant height from the apex to the center of the width of the rectangle is labeled 9 meters. Both heights are drawn as dotted lines. The sides that are not visible are shown in dashed lines.
What is the length of the pyramid?
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