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# Calculate The Surface Area of A Pyramid With A Rectangular Base

Last updated: Saturday, April 29, 2023
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Equilateral Triangular Base
Tetrahedron
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Hexagonal Base

A pyramid with a rectangular base is a captivating three-dimensional geometric figure that features a flat, rectangular base connected to a single apex point by four triangular lateral faces. This intriguing structure has inspired various applications in mathematics, physics, and science, as well as engineering and architecture. Within the context of surface area, the concept refers to the total area covering the external faces of the pyramid, which is of great significance for understanding its properties and practical applications.

In mathematics, the study of pyramids with rectangular bases provides insight into the properties of three-dimensional shapes, solid geometry, and the relationships between different types of polygons. These concepts are essential for a deeper understanding of geometry and its real-world applications. In physics, the surface area of a pyramid with a rectangular base can be used to analyze and predict properties such as center of mass, stability, and stress distribution, which are vital for the design and construction of structures and objects.

In science, the study of such pyramids has contributed to the development of crystallography, where the geometry of crystal structures and their surface area properties are essential for understanding the arrangement of atoms, ions, or molecules. This knowledge is crucial for advancements in material science, pharmaceuticals, and nanotechnology. In architecture, pyramids with rectangular bases have inspired the design of monumental structures such as the Louvre Pyramid in Paris, showcasing the combination of aesthetics and functionality.

The surface area of a pyramid with a rectangular base is the sum of the areas of all 4 triangular faces and the area of the rectangular base.

The formula for determining the surface area of a pyramid with a rectangular base is defined as:
$$SA$$ $$=$$ $$L$$ $$\cdot$$ $$W$$ $$+$$ $$L$$ $$\cdot$$ $$\sqrt{(\dfrac{W}{2})^2 + H^2}$$ $$+$$ $$W$$ $$\cdot$$ $$\sqrt{(\dfrac{L}{2})^2 + H^2}$$
$$SA$$: the surface area of the pyramid
$$L$$: the length of the longer side of the base
$$W$$: the length of the shorter side of the base
$$H$$: the height of the pyramid
The SI unit of surface area is: $$square \text{ } meter\text{ }(m^2)$$

## Find $$SA$$

Use this calculator to determine the surface area of a rectangular pyramid when the sides of the base and the height are given.
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the length of the longer side of the base
$$L$$
$$meter$$
the length of the shorter side of the base
$$W$$
$$meter$$
the height of the pyramid
$$H$$
$$meter$$
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