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Determine the surface area of the given regular pyramid.
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The surface area is found by calculating the lateral surface area and the base area and adding them together.
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As this pyramid is a regular pyramid and its base has four sides, its base is a square.
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Therefore, all four sides of its base are the same.
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The base area is therefore found by multiplying 31 by 31.
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Now letβs consider the lateral surface area.
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The formula for finding the lateral surface area of a pyramid is a half ππ, where π is the perimeter of the base and π is the slant height of the pyramid.
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The slant height of the pyramid has been given to us; itβs 36 centimetres.
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Remembering that the base of this pyramid is a square, its perimeter can be found by multiplying the side length by four.
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Now, letβs substitute the values of π and π into our calculation of the surface area.
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We have one-half multiplied by 124 multiplied by 36 for the lateral surface area.
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And as before, the base area is 31 multiplied by 31.
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Evaluating each of these terms gives 2232 plus 961.
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Finally, summing these two terms and including the units for surface area gives our answer to the problem, 3193 centimetres squared.