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  2. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    Interior angle Δθ = θ 1 −θ 2. The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines, which states that where is the angle between sides and . [45] When is radians or 90°, then , and the formula reduces to the usual Pythagorean theorem.

  3. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    That is, the area of the rectangle is the length multiplied by the width. As a special case, as l = w in the case of a square, the area of a square with side length s is given by the formula: [1] [2] A = s 2 (square). The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a ...

  4. 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. A rectangle with four sides of equal length is a ...

  5. Area of a triangle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_triangle

    In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denotes any side, and "height" denotes the length of a perpendicular ...

  6. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Since x 2 represents the area of a square with side of length x, and bx represents the area of a rectangle with sides b and x, the process of completing the square can be viewed as visual manipulation of rectangles. Simple attempts to combine the x 2 and the bx rectangles into a larger square result in a missing corner.

  7. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the coordinates making up the ...

  8. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    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 ...

  9. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    The area formula for a triangle can be proven by cutting two copies of the triangle into pieces and rearranging them into a rectangle. In the Euclidean plane, area is defined by comparison with a square of side length ⁠ ⁠, which has area 1. There are several ways to calculate the area of an arbitrary triangle.

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