12.+Area+&+Perimeter


 * Perimeter **

**Perimeter ** is the distance around the outside of a figure. To find the perimeter of a figure, just add up all the sides of the shape. If any of the sides are the same, multiply the measure of one side by the total number of sides that are the same length and then add the rest of the sides that are not the same length. The perimeter is always measured in units. Example: The perimeter of this square is        or. Example:

The perimeter of this rectangle is

11.3 + 11.3 + 25.4 + 25.4 = 73.4cm or (2 x 11.3) + (2 x 25.4) = 22.6 + 50.8 = 73.4cm.  Either method works to find the perimeter, so pick whichever one you feel more comfortable with.  The side length multiplied by the number of equal sides comes in handy, especially when all the sides match.

Example: <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">For this regular pentagon, all you need to do to find the perimeter is multiply the side length, 12.8cm, by the number of sides, 5. <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">12.8 x 5 = 64.0cm
 * <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 200%;">Area **

**<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area **<span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;"> is the amount of surface a figure covers. It is measured in square units. There are different formulas to find the area of different shapes, such as rectangles, parallelograms, and triangles. <span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">To find the area of this rectangle, you can either count the number of squares, 40, or you can use the formula,  <span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area = Base x Height     <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">A = 8 x 5 = 40cm <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 140%; vertical-align: super;">2      <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The same formula applies for squares and even other parallelograms. <span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Example: <span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">In a parallelogram, the base is the length, 6.5in, and the height is always the line perpendicular to the base, 2.1in. The 3.2in is not the height of the parallelogram. <span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area = Base x Height    <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area = 6.5 x 2.1 = 13.65in <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%; vertical-align: super;">2 <span style="color: #ff0028; font-family: 'Times New Roman',Times,serif; font-size: 140%;">As for other figures, there are different formulas that can be used to find the area. For example, the triangle has the formula, <span style="color: #ff0028; font-family: 'Times New Roman',Times,serif; font-size: 140%;">because a triangle is half of a parallelogram.

<span style="color: #008000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The triangle fills half of the rectangle, so it's area is half area of the rectangle too.

<span style="color: #800080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area =



<span style="color: #008080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Area =


 * <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 180%;">Circles **

<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">You can find the area and perimeter, circumference, of a circle, just like you can for other polygons. You just have different formulas to use to figure them out. Before you can learn the formulas, you first need to learn some vocabulary.

<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The **radius** is the distance from the center of the circle to any point on the outside of the circle. The **diameter** is the distance from one side of the circle to the other side, passing through the center.
 * Pi** is a the ratio from the diameter to the circumference. The value of pi is approximately 3.14.
 * Circumference** is the distance around the outside of the circle.

<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The formula of the circumference is pi times the diameter. **C = πd or c =** **2πr**

<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">The area of the circle is calculated as pi times the radius squared. **A = πr** **<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 ** <span style="color: #800000; display: block; font-family: 'Times New Roman',Times,serif; font-size: 140%; text-align: center;">**C =** **2πr** <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">C = 2(3.14)(4)  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">C = 25.12cm <span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 140%;">**A = πr** **<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 ** <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">A = (3.14)(4) <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2 <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">A = (3.14)(16)  <span style="font-family: 'Times New Roman',Times,serif; font-size: 140%;">A = 50.24cm <span style="font-family: 'Times New Roman',Times,serif; font-size: 120%; vertical-align: super;">2

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Area and Perimeter Game] - This website incorporates a lesson on area and perimeter, and then provides some problems for you to practice with. It is a great refresher website for you to use. <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Shape Explorer - Find the Area & Perimeter] - This website requires you to find the area and the perimeter of different irregular polygons. The site draws the shapes on a grid, so finding both the area and the perimeter should be pretty straightforward.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Triangle Builder - Area] - This activity has you practicing finding the area of different triangles. The website provides a triangle on a grid, and you need to come up with the area, using the area of a triangle formula.

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|Geometry Quiz] - This quiz tests your knowledge of finding area and perimeter of rectangles, triangles, and circles.

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**//<span style="color: #800000; font-family: 'Times New Roman',Times,serif; font-size: 160%;">If you have any questions about area and perimeter, please feel free to use the discussion tab at the top of this page, and either myself, or one of your classmates, can answer them for you. //**

<span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">Geometry and Measurement: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">describe relationships, communicate ideas and solve problems. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">4. Use rectangles as basic shapes to model and develop formulas for finding the area <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">of triangles, parallelograms and trapezoids. <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure <span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">. <span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 120%;">lkasdlks <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">8. Select and use appropriate strategies, tools and units to estimate and solve <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">measurement problems involving length, perimeter, area, volume, capacity,  <span style="color: #000080; font-family: 'Times New Roman',Times,serif; font-size: 140%;">mass and weight.
 * <span style="color: #2c0080; font-family: 'Times New Roman',Times,serif; font-size: 160%;">Connecticut 6th Grade Mathematics Curriculum Standards: **

<span style="color: #0000ff; font-family: 'Times New Roman',Times,serif; font-size: 140%;">[|CT Mathematics Standards]