The proper name for what many people call a diamond shape is actually a rhombus -- a four-sided figure where every side is the same length and each opposite pair of angles is equal. Rhombuses show up in everything from kites to floor tiles and, depending on which information you have about the rhombus in question, you can calculate its area in the following three ways.
Multiply the altitude of the diamond times the length of one of its sides. The altitude is the distance between any two opposite sides of the diamond. So if the diamond has an altitude of 8 inches and its sides are each 10 inches long, its area is 8 * 10 = 80 inches squared.
Square the length of any side, and multiply the result by the sine of one of the angles inside the diamond. The sine of an angle can be determined using a scientific calculator or from a list of sines of common angles. So if the diamond has a side of length 6 inches and one of its angles measure 30 degrees with a sine of 0.5, the length of the side squared is 6 * 6 = 36, which multiplied by the sine gives you 36 * 0.5 = 18 inches squared as the area.
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Multiply the lengths of the diagonals inside the diamond -- that is, the two lines between opposite vertices -- together. Divide the result by 2 to get the area. So for a diamond with diagonal lengths of 8 inches and 4 inches, its area would be (8 * 4)/2 = 16 inches squared.
It doesn't matter which side you use for the "square the length of any side" method, because all sides of a rhombus are the same length. Similarly, which angle you use for that method doesn't matter either because adjacent angles of a rhombus are always supplementary, which means every angle inside a rhombus has an identical sine value.