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What is the height of the stainless-steel pyramid-shaped patio heater?

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A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 6 feet. The slant height is 10 feet. What is the height of the heater? Round to the nearest tenth of a foot.

The height of the heater is about __ feet. (Round to the nearest tenth as needed.)




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    1 Answer

    1. Quizzma Team

      To find the height of the square pyramid-shaped patio heater, we can use the Pythagorean theorem. The relationship between the height (h), the slant height (l), and half the length of the base (b/2) can be expressed as:

      [ l^2 = h^2 + (b/2)^2 ]

      Given:

      – The length of one side of the base (b) = 6 feet, so half of the base (b/2) = 3 feet.

      – The slant height (l) = 10 feet.

      Now, plug in the values:

      [ 10^2 = h^2 + 3^2 ]

      [ 100 = h^2 + 9 ]

      [ h^2 = 100 – 9 ]

      [ h^2 = 91 ]

      Now, take the square root to find the height:

      [ h = sqrt{91} approx 9.5 text{ feet} ]

      So, the height of the heater is approximately 9.5 feet.

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