The lateral edge of a regular hexagonal pyramid is 14 cm and is inclined at an angle of 30 degrees

univerkov | March 19, 2021 | education

The lateral edge of a regular hexagonal pyramid is 14 cm and is inclined at an angle of 30 degrees to the base. Calculate the area of the circle around the hexagon.

The diameter of the circumscribed circle near a regular hexagon is its large diagonal AD.

Since all the side edges of the pyramid are equal to 14 cm, the triangle ASD is isosceles at the angle at the apex S equal to: angle ASD = (180 – 30 – 30) = 120.

By the cosine theorem, we define the length of the base AD.

AD ^ 2 = AS ^ 2 + SD ^ 2 – 2 * AS * SD * Cos120 = 196 + 196 – 2 * 14 * 14 * (-1/2) = 392 + 196 = 588.

AD = 14 * √3 cm.

Then the area of the circle is: S = π * AD ^ 2/4 = π * 147 cm2.

Answer: The area of a circle is π * 147 cm2.

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