area

Determining Perimeter & Area

Suppose you have a yard and want to put up a fence. You need to know how much fencing material to purchase, so you must know the length around the yard, or its perimeter. If you want to lay down sod, you would want to know how much sod you need for the project by determining the size or area of the yard. Because the shape of things (like yards) vary, it is important to understand how to find out where to begin measuring. The following information details how to find the perimeter and area of the most common shapes. For more detailed explanations of these concepts go to the links at the bottom of this page.

Square

The perimeter of a square is equal to 4 times the length of a side.
The area of a square is equal to the length of a side raised to the 2nd power (the length of one side multiplied by any other side).

Rectangle

Let 'a' and 'b' represent the length of two adjacent sides of a rectangle. The perimeter of a rectangle is equal to 2 * [a+b], ( the length of one side added to the length of an adjacent side, then multiplied by 2).
The area of a rectangle is equal to [a * b], (the length of one side multiplied by an adjacent side.

Triangle

Let 'AB' represent the base of the triangle, and 'CD' represent the altitude (h). The perimeter of a triangle is equal to the sum of the length of the three sides [AB+BC+CA].
The area of a triangle is equal to 1/2[AB * h], (the length of the base multiplied by the altitude, then multiplied by .5).

Circle
*Terms to know: pi (p) is the ratio of the circumference to the diameter in all circles [pi always = 3.141...]; the diameter is the distance across a circle; and the radius is the distance from the center of a circle to any point on its edge).
The perimeter of a circle is called the circumference which is equal to pi multiplied by the diameter (p* d).
The area of a circle is equal to p* r²(the length of the radius squared, then multiplied by 3.141...).

Trapezoid

Let 'ABCD' represent a trapezoid where AB and DC are the bases; DE and CF are the altitudes (h). The perimeter of a trapezoid is the sum of the length of all sides [AB+BC+CD+DA].
The area of a trapezoid is equal to 1/2 *[AB +CD]* h, (add the lengths of each base together, multiply by the length of the altitude, then multiply by .5)

Polygons

Polygons are figures with many sides and many angles (pentagon 5, hexagon 6, octagon 8). The perimeter of a polygon is equal to the sum of the length of all sides [AB+BC+CD+DE+EA, etc.].
The area of a polygon is most easily obtained by breaking the figure into other measurable shapes (squares, rectangles, and/or triangles), then adding the areas together.

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