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Questions and Answers
What is the characteristic feature of a pyramid's base?
What is the characteristic feature of a pyramid's base?
What is the formula to find the area of a triangular base?
What is the formula to find the area of a triangular base?
What is the label for the height of a pyramid?
What is the label for the height of a pyramid?
What is the measurement that tells you the length of the side from the top to the edge of the base?
What is the measurement that tells you the length of the side from the top to the edge of the base?
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What is the formula to find the perimeter of a base?
What is the formula to find the perimeter of a base?
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What is the formula for finding the surface area of a pyramid?
What is the formula for finding the surface area of a pyramid?
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What is the base area of the pyramid in the sample problem?
What is the base area of the pyramid in the sample problem?
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What is the unit of measurement for volume?
What is the unit of measurement for volume?
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What is the formula for finding the volume of a pyramid?
What is the formula for finding the volume of a pyramid?
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What is the value of the slant length in the sample problem?
What is the value of the slant length in the sample problem?
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Study Notes
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).
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Description
Learn about pyramids, 3-dimensional objects with a polygonal base and sides meeting at an apex. Explore square pyramids and how they're named after their bases.
