Pyramid Area and Measurements

• Pyramids are 3D objects
• They have a polygonal base
• Sides meet at a single point on top, called the apex
• Egyptian pyramids have a square base
• Pyramids are named after the shape of their base
• A pyramid with a triangular base is a triangular pyramid

Pyramid Measurements

• Four key measurements are needed to find surface area and volume

Area of the Base (B)

• For a square base, multiply the length and width to find the area
• For a triangle base, multiply the length and height, and divide by two
• Some problems provide the area, while others require calculation using the appropriate formula

Perimeter of the Base (P)

• Add all the edge lengths around the base
• A base might have three, four, or more sides

Height (h)

• Measures how tall the pyramid stands

Slant Length (s)

• Measures the length of the side from the apex down to the edge of the base

Surface Area

• The formula to find the total area of all surfaces: B + (P * s) / 2
• Multiply the base perimeter by the slant height, divide by 2, and add the result to the base area

Example Calculation of Surface Area

• Square pyramid with each side measuring 750 feet, a height of 500 feet, and a slant length of 650 feet
• Base Area (B): 750 * 750 = 562,500 sq ft
• Base Perimeter (P): 750 + 750 + 750 + 750 = 3,000 ft
• Surface Area Calculation: 562,500 + (3,000 * 650) / 2 = 1,537,500 sq ft
• Area is measured in square units

Volume

• The space inside the pyramid is calculated using the formula: (B * h) / 3
• Multiply the base area by the height and divide by 3

Example Calculation of Volume

• Using the same pyramid parameters, base area = 562,500 sq ft and height = 500 ft
• Volume Calculation: (562,500 * 500) / 3 = 93,750,000 cubic feet
• Volume is measured in cubic units