Video: Finding the Total Surface Area of a Square Pyramid given Its Base Side and Its Slant Height

Determine the surface area of the given regular pyramid.

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Video Transcript

Determine the surface area of the given regular pyramid.

The surface area is found by calculating the lateral surface area and the base area and adding them together. As this pyramid is a regular pyramid and its base has four sides, its base is a square. Therefore, all four sides of its base are the same. The base area is therefore found by multiplying 31 by 31.

Now let’s consider the lateral surface area. The formula for finding the lateral surface area of a pyramid is a half 𝑃𝑙, where 𝑃 is the perimeter of the base and 𝑙 is the slant height of the pyramid. The slant height of the pyramid has been given to us; it’s 36 centimetres. Remembering that the base of this pyramid is a square, its perimeter can be found by multiplying the side length by four.

Now, let’s substitute the values of 𝑃 and 𝑙 into our calculation of the surface area. We have one-half multiplied by 124 multiplied by 36 for the lateral surface area. And as before, the base area is 31 multiplied by 31. Evaluating each of these terms gives 2232 plus 961. Finally, summing these two terms and including the units for surface area gives our answer to the problem, 3193 centimetres squared.

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