Geometry: Pyramids

Pyramids

• A pyramid is a 3-dimensional object with a polygonal base and sides that meet at one point at the top called an apex.
• The pyramids of Egypt have a square base and are called square pyramids.
• Pyramids are named after their bases, e.g., triangular pyramid if the base is a triangle.

Measurements

• There are four important measurements for pyramids: area of the base (B), perimeter of the base (P), height (h), and slant length (s).
• The area of the base is calculated using the formula for the base shape (e.g., square: length × width, triangle: length × height ÷ 2).
• The perimeter of the base is calculated by adding up the edges of the base.
• The height measures how tall the pyramid stands.
• The slant length is the length of the side from the top to the edge of the base.

Surface Area

• The formula for surface area is: Surface Area = B + (P × s)/2.
• The formula uses the area of the base, perimeter of the base, and slant length.

Example Problem

• A sample problem: calculate the surface area of a square pyramid with a base side of 750 feet, height of 500 feet, and slant length of 650 feet.
• The solution involves calculating the base area (562,500 sq ft) and perimeter (3,000 ft), then plugging the values into the formula.

Volume

• The formula for volume is: Volume = (B × h)/3.
• The formula uses the area of the base and the height.
• A sample problem: calculate the volume of the same pyramid (answer: 93,750,000 feet cubed).