Pyramid Geometry Concepts

This video tutorial explains how to calculate the surface area and volume of a hexagonal pyramid. It begins with an introduction to the geometric properties of hexagonal pyramids, including the base, height, apothem, and slant height. The video then provides two detailed examples, demonstrating the step-by-step process of using the Pythagorean theorem and geometric formulas to find the surface area and volume. The tutorial emphasizes the importance of identifying given values and applying the correct formulas.

What is the base shape of a hexagonal pyramid?

• Pentagon

• Hexagon

• Square

• Triangle

In a hexagonal pyramid, what is the term for the distance from the vertex to the center of the base?

• Radius

• Slant Height

• Height

• Apothem

Which theorem is used to relate the height, apothem, and slant height in a pyramid?

• Fermat's Last Theorem

• Binomial Theorem

• Pythagorean Theorem

• Fundamental Theorem of Calculus

What is the formula for the surface area of a pyramid?

• Base area + perimeter x height

• 1/3 base area x height

• Base area x height

• Base area + 1/2 perimeter x slant height

What is the formula for the volume of a pyramid?

• Base area x height

• 1/3 base area x height

• Base area + 1/2 perimeter x slant height

• Base area + perimeter x height

In Example 1, what is the given height of the pyramid?

• 9 units

• 6 units

• 12 units

• 15 units

In Example 1, what is the perimeter of the hexagonal base?

• 24 units

• 18 units

• 30 units

• 36 units

In Example 1, what is the area of the base of the pyramid?

• 54 square root 3

• 90 square root 3

• 36 square root 3

• 72 square root 3

In Example 1, what is the calculated surface area of the pyramid?

• 180.50 units squared

• 200.50 units squared

• 280.50 units squared

• 300.50 units squared

In Example 1, what is the calculated volume of the pyramid?

• 300.50 units cubed

• 180.50 units cubed

• 200.50 units cubed

• 280.50 units cubed