Find the slant height x of the pyramid shown, to the nearest tenth.
A right square pyramid is shown. The sides of the square base measure 7 millimeters. A dashed line which is labeled x extends from the middle of a side of the base along a triangular surface to the vertex at the top of the pyramid. A small square is located where the dashed line intersects with the base. The pyramid height is 6 millimeters.
(1 point)
Responses
4.35 mm
4.35 mm
9.2 mm
9.2 mm
6.9 mm
6.9 mm
3.6 mm
3.6 mm
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To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height forms a right triangle with one leg measuring half the length of a side of the base (3.5 mm) and the other leg measuring the height of the pyramid (6 mm).
So, we have:
a^2 + b^2 = c^2
(3.5 mm)^2 + (6 mm)^2 = c^2
12.25 mm^2 + 36 mm^2 = c^2
48.25 mm^2 = c^2
Taking the square root of both sides, we find:
c = √48.25 mm
c ≈ 6.9 mm
Therefore, the slant height x of the pyramid is approximately 6.9 mm, to the nearest tenth.