How to Find the Area of the Base of a Pyramid
Pyramids are three-dimensional objects where a base is connected to a single apex. The shape of the pyramid base determines the type of pyramid. A triangular pyramid results from a triangular base connected to a common apex by three additional sides. The four sides of the square pyramid join the base to a common apex. The area of the pyramid base is calculated by measuring the sides of the base and using the appropriate formula for that particular shape.
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Instructions
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Base of a Regular Triangular Pyramid
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Measure the sides of the triangle drawn. A regular triangular pyramid will have base sides of equal length and form an equilateral triangle.
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Square the length of a side of the triangle. For example, a triangular pyramid with a length of 5 cm along each side of its base would be squared to 25 (5 x 5 = 25).
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Multiply the square of the length by the square root of three. Continuing the example, 25 multiplied by the square root of three produces 43.3 (25√3 = 43.3).
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Divide the previous product by four. The final solution for the area of a regular triangular pyramid with sides that are 5 cm long is 10.8 square inches (43.3 ÷ 4 = 10.8 square inches). This is the same method for measuring the area of any equilateral triangle.
Base of a Regular Square Pyramid
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Identify the type of pyramid. Regular pyramids have a base shaped as a regular polygon such as a square. Irregular pyramids will have a base shaped as an irregular polygon. Square pyramids will have a base shaped as a square.
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Measure the sides of the base of the pyramid. Again, a regular pyramid will have sides of equal length and in this case form a square.
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Multiply the length of one base side by another base side. Because these measurements are the same for a square, the length can simply be squared. A square pyramid with equal lengths along its base of 5 cm will have an area of 25 square centimeters (5 cm x 5 cm = 25 square cm).
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References
- Photo Credit pyramids image by Horticulture from Fotolia.com
