Understanding the surface area of pyramids is crucial in geometry. This overview covers the calculation of surface areas for pyramids with different base shapes, such as square, triangular, and hexagonal. It explains the components of pyramids, including the base, apex, and slant height, and provides formulas for both lateral and total surface area. Practical examples illustrate how to apply these formulas to find the surface area of pyramids in real-world scenarios.
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A pyramid is a three-dimensional shape with a polygonal base and triangular faces that meet at a common vertex
The height of a pyramid is the perpendicular distance from the base to the apex, while the slant height is the length from the apex to the midpoint of a side of the base
Pyramids are named after the shape of their base, such as square, triangular, or hexagonal pyramids
The lateral surface area (LSA) is calculated by multiplying half the perimeter of the base by the slant height, while the total surface area (TSA) includes the area of the base and is found by adding the LSA to the base area
The TSA of a triangular base pyramid is the sum of the base area and half the perimeter of the base multiplied by the slant height
The TSA of a square base pyramid is the sum of the base area and twice the base length multiplied by the slant height
The TSA of a hexagonal base pyramid is the sum of three times the base length multiplied by the apothem and three times the base length multiplied by the slant height
For a square pyramid with a base side length of 14 cm and a slant height of 20 cm, the LSA can be found by multiplying 4 by 14 and dividing by 2, resulting in 56 cm^2
The formulas for TSA and LSA can be rearranged to solve for unknown values, such as the base area or slant height
Mastery of the concepts and formulas for calculating surface area of pyramids is useful in both educational settings and practical applications
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Pyramid Base Shape Names
Pyramids named for base shape: square, triangular, hexagonal.
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Pyramid Height vs Slant Height
Height: base to apex. Slant Height: apex to base midpoint.
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Surface Area Calculation Components
Surface Area = Base Area + Sum of Triangular Faces' Areas.
