Overview:
Area and perimeter are two important measurements of a geometric figure. The area is the number of units enclosed within its surface, and the measurement of the distance around its boundaries is the perimeter. The perimeter is usually measured in units and the area, in square units.
Area and Perimeter of Rectangles
The area of a rectangle is length times width and will equal square units. If a rectangle is 8 in x 10 in, its area will be 80 square inches. Its perimeter will be the sum of all 4 sides, or 8 + 8 + 10 +10 or 36 inches. The area of a rectangle depends on its shape. If a rectangle is 6 in X 12 in, its perimeter will be 6 + 6 + 12 +12 or 36 inches, but its area will be 72 square inches. If a rectangle is 16 inches by 2 inches, its perimeter will be 16 +16 +2 +2 or 36 inches, but its area will be 32 square inches. Even when the perimeter of rectangles are the same, the area can vary depending on the shape of the rectangle.
Area and Perimeter of Parallelograms
Other types of four-sided figures are shaped differently from rectangles. Parallelograms do not have 900 angles at their vertices, so it is more difficult to measure their area due to their slanted sides. It can be shown that the height times the base of the parallelogram is similar to the length times the width of a rectangle, and so measures the area. The perimeter is the sum of all four sides.
Area and Perimeter of Triangles
The perimeter of a triangle is the sum of all three sides. The formula for the area is 1/2 times the base times the height of the triangle. If a triangle and an exact copy of that triangle are put together so that they form a parallelogram, each triangle takes up half the area of the parallelogram. Suppose the base of a triangle is equal to 5 inches and the height is equal to 2 inches. The area will equal 1/2 X 5 X 2, or 5 square inches.
Area and Perimeter of Other Polygons
The areas of other polygons can be measured by measuring the areas of all the other shapes that make them up and then combining them. The perimeter is the sum of the measurement of all sides of the polygon. Even fairly irregular shapes can be divided into combinations of triangles, rectangles, unit squares, and others that are more easily measured.
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