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  2. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Consider completing the square for the equation + =. 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.

  3. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    Calculation of the area of a square whose length and width are 1 metre would be: 1 metre × 1 metre = 1 m 2. and so, a rectangle with different sides (say length of 3 metres and width of 2 metres) would have an area in square units that can be calculated as: 3 metres × 2 metres = 6 m 2. This is equivalent to 6 million square millimetres.

  4. Lattice multiplication - Wikipedia

    en.wikipedia.org/wiki/Lattice_multiplication

    A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).

  5. Shoelace formula - Wikipedia

    en.wikipedia.org/wiki/Shoelace_formula

    Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). 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]

  6. Square (algebra) - Wikipedia

    en.wikipedia.org/wiki/Square_(algebra)

    5⋅5, or 5 2 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square. In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation.

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  9. Proportional reasoning - Wikipedia

    en.wikipedia.org/wiki/Proportional_reasoning

    Someone with knowledge about the area of triangles might reason: "Initially the area of the water forming the triangle is 12 since ⁠ 1 / 2 ⁠ × 4 × 6 = 12. The amount of water doesn't change so the area won't change. So the answer is 3 because ⁠ 1 / 2 ⁠ × 3 × 8 = 12." A correct multiplicative answer is relatively rare.

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