Question

The base of a regular pyramid is a hexagon. The figure shows a regular hexagon with center C. An apothem is shown as a dashed segment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 8 centimeters. The angle formed by the edge and the segment measure 60 degrees. What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.

Answer 1

Answer: The area of the hexagonal base is 96 square roots of 3.

The hexagon is divided into 6 congruent triangles. All we have to do is find the area of one of these shapes and multiply by 6.

The base of each triangle is 8 because the triangles are equilateral and one side is already given. The height is 4 square roots of 3 because it is a 30/6090 triangle.

To find the area, we multiply 8 x 4 square roots of 3 and divide by 2 to get 16 square roots of 3.

Multiply 16 by 6 and you get 96 square roots of 3.