The diagonal of the base of a regular quadrangular pyramid is 8√2 cm, and the apothem makes

| September 24, 2021 | education

The diagonal of the base of a regular quadrangular pyramid is 8√2 cm, and the apothem makes an angle of 60 ° with the base plane. Find the total surface area of the pyramid.

To find out the total surface area of the pyramid in question, we will use the formula (we take into account that there is a square at the base): S = Side + Sb = 0.5 * Rosn * h + 0.5 * d ^ 2 = 0.5 * (d * 2 * √2) * (0.5 * a * cosα) + 0.5 * d ^ 2 = 0.5 * d * √2 * d * cosα / √2 + 0.5 * d ^ 2 = 0, 5 * d ^ 2 * cosα + 0.5 * d ^ 2 = 0.5 * d ^ 2 * (cosα + 1).

Data: d – base diagonal (d = 8 * √2 cm); α is the angle between the apothem and the base plane (α = 60º).

Let’s perform the calculation: S = 0.5 * d ^ 2 * (cosα + 1) = 0.5 * (8 * √2) ^ 2 * (cos 60º + 1) = 64 * 1.5 = 96 cm2.

Answer: The total surface area of the considered pyramid is 96 cm2.



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