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The area of an isosceles (or any) trapezoid is equal to the average of the lengths of the base and top (the parallel sides) times the height. In the adjacent diagram, if we write AD = a, and BC = b, and the height h is the length of a line segment between AD and BC that is perpendicular to them, then the area K is
Heron's formula. A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, the area is [1] It is named after first-century engineer Heron of Alexandria (or Hero) who ...
The area K of a trapezoid is given by [13] = + = where a and b are the lengths of the parallel sides, h is the height (the perpendicular distance between these sides), and m is the arithmetic mean of the lengths of the two parallel sides.
Frustum. In geometry, a frustum (Latin for 'morsel'); [a] (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone ...
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids ...
This is not true for other lines through the centroid; the greatest departure from the equal-area division occurs when a line through the centroid is parallel to a side of the triangle, creating a smaller triangle and a trapezoid; in this case the trapezoid's area is that of the original triangle. [18]
A skeletal pyramid with its base highlighted. In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure. [1] This term is commonly applied in plane geometry to triangles, parallelograms ...
The volume of a prism is the product of the area of the base by the height, i.e. the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance). The volume is therefore: =, where B is the base area and h is the height.