Area+&+Perimeter

Similar to the [|rectangle], finding the area of a parallogram requires two known distances. We need to know its height and the length of the side that is perpendicular to the height, called the base of the parallelogram. If we start with a typical parallelogram, we can make a few alterations to it in order to calculate its area. If we cut it along its height, we can remove a portion that is a right triangle. If we move this right triangle to the opposite side of the figure, it will fit perfectly and create a rectangle. Since we already know the [|area of a rectangle](see above) to be A = lw, let us apply it to the newly altered parallelogram. The base of the original parallogram is now the length of the rectangle. The height of the parallelogram is now the width of the rectangle. Using the names base and height instead of length and width, we see that the area of a parallogram is A = bh. Example 1: If b = 7 in and h = 4 in, then the area would be A = (7 in)(4 in) = 28 in2. Example 2: If b = 12 m and h = 8 m, then the area would be A = (12 m)(8 m) = 96 m2.
 * **Area of Parallelograms** || A = bh ||
 * A parallelogram is a quadrilateral (four-sided figure) that has opposite sides that are parallel. || [[image:http://www.mathguide.com/lessons/pic-parallelogramT.gif width="242" height="159"]]**Parallelogram** ||
 * [[image:http://www.mathguide.com/lessons/pic-demoparallelogram2.gif width="384" height="303" align="center" caption="Transformation: Parallelogram to Rectangle"]] ||

A triangle can be defined by the length of its base and its height. The height is always perpendicular to the base, exactly like the base and height of a [|parallelogram]. We can find the area of a triangle by performing three tasks. First, we duplicate the original triangle. Second, we rotate this duplicate triangle 180 degrees. Third, place the rotated duplicate triangle next to the original triangle so that they fit snuggly together to form a parallelogram. We know the area of a parallelogram to be A = bh. In our newly formed diagram, we can use those same distances to arrive at the exact same area for the two-triangle area. However, if we want to know the area of one of those triangles instead of the whole parallelogram, we have to divide the area into two equal portions since the triangles
 * **Area of Triangles** || A = ½bh ||
 * A triangle is a three-sided polygon. || [[image:http://www.mathguide.com/lessons/pic-triangleT.gif width="268" height="131" align="center"]]
 * Triangle** ||
 * Triangle** ||
 * [[image:http://www.mathguide.com/lessons/pic-demotriangle.gif width="300" height="385" align="center"]] ||

**Games for Area & Perimeter** []

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**Practice Sheets**