At the gate of a stadium there are two pillars of height 10ft. whose all 4 sides are visible. There is a pyramid on top of height of each pyramid 2ft. Base of each pillar and pyramid is 4ft.*4ft. Find slant height of pyramid
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Answer:
2.83 feet.
Step-by-step explanation:
To find the slant height of the pyramid on top of each pillar, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and half the width of the base.
Given:
Height of the pyramid (h) = 2 ft
Width of the base (w) = 4 ft
Let's denote the slant height as 's'.
Using the Pythagorean theorem, we have:
s^2 = h^2 + (w/2)^2
Substituting the given values:
s^2 = 2^2 + (4/2)^2
s^2 = 4 + 2^2
s^2 = 4 + 4
s^2 = 8
Taking the square root of both sides:
s = √8
Simplifying the square root:
s ≈ 2.83 ft
Therefore, the slant height of the pyramid is approximately 2.83 feet.