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  2. Parallelogram - Wikipedia

    en.wikipedia.org/wiki/Parallelogram

    The area of the parallelogram is the area of the blue region, which is the interior of the parallelogram. The base × height area formula can also be derived using the figure to the right. The area K of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the ...

  3. Base (geometry) - Wikipedia

    en.wikipedia.org/wiki/Base_(geometry)

    By this usage, the area of a parallelogram or the volume of a prism or cylinder can be calculated by multiplying its "base" by its height; likewise, the areas of triangles and the volumes of cones and pyramids are fractions of the products of their bases and heights. Some figures have two parallel bases (such as trapezoids and frustums), both ...

  4. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    By analogy, it relates to a parallelogram just as a cube relates to a square. [a] Three equivalent definitions of parallelepiped are a hexahedron with three pairs of parallel faces, a polyhedron with six faces , each of which is a parallelogram, and; a prism of which the base is a parallelogram.

  5. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    Each sector is approximately triangular in shape, and the sectors can be rearranged to form an approximate parallelogram. The height of this parallelogram is r, and the width is half the circumference of the circle, or πr. Thus, the total area of the circle is πr 2: [2] A = πr 2 (circle).

  6. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: ‖ ‖ + ‖ ‖ = ‖ + ‖ + ‖ ‖,.. The parallelogram law is equivalent to the seemingly weaker statement: ‖ ‖ + ‖ ‖ ‖ + ‖ + ‖ ‖, because the reverse inequality can be obtained from it by substituting (+) for , and () for , and then simplifying.

  7. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    The height (or altitude) is the perpendicular distance between the bases. In the case that the two bases have different lengths (a ≠ b), the height of a trapezoid h can be determined by the length of its four sides using the formula [13] = () () | |

  8. Pappus's area theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_area_theorem

    The extended parallelogram sides DE and FG intersect at H. The line segment AH now "becomes" the side of the third parallelogram BCML attached to the triangle side BC, i.e., one constructs line segments BL and CM over BC, such that BL and CM are a parallel and equal in length to AH.

  9. Rectangle - Wikipedia

    en.wikipedia.org/wiki/Rectangle

    In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles.It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle.