Calculate the total surface area of a regular quadrangular pyramid, each edge of which is 5 dm.
| April 26, 2021 | education
Since the pyramid is correct, there is a square at its base.
Determine the area of the base of the pyramid.
Sbn = AB * AD = 5 * 5 = 25 cm2.
The side faces of the pyramid are four equal, equilateral triangles.
Determine the area of one side face.
We apply the formula for the area of an equilateral triangle S = a ^ 2 * √3 / 4, where a is the length of the side of the triangle.
Streug = 25 * √3 / 4 cm2.
Then S side = 4 * Streug = (25 * √3 / 4) * 4 = 25 * √3 cm2.
Determine the total area of the pyramid.
Spol = Sside + Sbn = 25 * √3 + 25 = 25 * (1 + √3) cm2.
Answer: The total area of the pyramid is 25 * (1 + √3) cm2.
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