Perimeter_Area

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__LETS HAVE  SOME  FUN  WITH  PERIMETER AND AREA !!!!!!!!!!!  __

__DEFINITIONS OF AREA AND PERIMETER:__

__AREA :__ The area of a figure measures the size of the region enclosed by the figure This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.

__PERIMETER;__ margin: the boundray line or the area inside the boundary.

To find the area of a triangle is area= 1/2 x base x height

If //l// is the side-length of a square, the area of the square is //l//2 //or l// × //l//. Example: What is the area of a square having side-length 3.4? The area is the square of the side-length, which is 3.4 × 3.4 = 11.56.

The area of a rectangle is the product of its width and length. Example: What is the area of a rectangle having a length of 6 and a width of 2.2? The area is the product of these two side-lengths, which is 6 × 2.2 = 13.2.

The area of a parallelogram is //b// × //h//, where //b// is the length of the base of the parallelogram, and //h// is the corresponding height. To picture this, consider the parallelogram below: We can picture "cutting off" a triangle from one side and "pasting" it onto the other side to form a rectangle with side-lengths //b// and //h//. This rectangle has area //b// × //h//. Example: What is the area of a parallelogram having a base of 20 and a corresponding height of 7? The area is the product of a base and its corresponding height, which is 20 × 7 = 140.

If //a// and //b// are the lengths of the two parallel bases of a trapezoid, and //h// is its height, the area of the trapezoid is 1/2 × //h// × (//a + b//). To picture this, consider two identical trapezoids, and "turn" one around and "paste" it to the other along one side as pictured below: The figure formed is a parallelogram having an area of //h// × (//a// + //b//), which is twice the area of one of the trapezoids. Example: What is the area of a trapezoid having bases 12 and 8 and a height of 5? Using the formula for the area of a trapezoid, we see that the area is 1/2 × 5 × (12 + 8) = 1/2 × 5 × 20 = 1/2 × 100 = 50.

or Consider a triangle with base length //b// and height //h//. The area of the triangle is 1/2 × //b// × //h//. To picture this, we could take a second triangle identical to the first, then rotate it and "paste" it to the first triangle as pictured below: or The figure formed is a parallelogram with base length //b// and height //h//, and has area //b// × //h//. This area is twice that of the triangle, so the triangle has area 1/2 × //b// × //h//. Example: What is the area of the triangle below having a base of length 5.2 and a height of 4.2? The area of a triangle is half the product of its base and height, which is 1/2 ×5.2 × 4.2 = 2.6 × 4.2 = 10.92..

The area of a circle is Pi × //r//2 or Pi × //r// × //r//, where //r// is the length of its radius. Pi is a number that is approximately 3.14159. Example: What is the area of a circle having a radius of 4.2 cm, to the nearest tenth of a square cm? Using an approximation of 3.14159 for Pi, and the fact that the area of a circle is Pi × //r//2, the area of this circle is Pi × 4.22 3.14159 × 4.22 =55.41…square cm, which is 55.4 square cm when rounded to the nearest tenth.

The perimeter of a polygon is the sum of the lengths of all its sides. Example: What is the perimeter of a rectangle having side-lengths of 3.4 cm and 8.2 cm? Since a rectangle has 4 sides, and the opposite sides of a rectangle have the same length, a rectangle has 2 sides of length 3.4 cm, and 2 sides of length 8.2 cm. The sum of the lengths of all the sides of the rectangle is 3.4 + 3.4 + 8.2 + 8.2 = 23.2 cm. Example: What is the perimeter of a square having side-length 74 cm? Since a square has 4 sides of equal length, the perimeter of the square is 74 + 74 + 74 + 74 = 4 × 74 = 296. Example: What is the perimeter of a regular hexagon having side-length 2.5 m? A hexagon is a figure having 6 sides, and since this is a regular hexagon, each side has the same length, so the perimeter of the hexagon is 2.5 + 2.5 + 2.5 + 2.5 + 2.5 + 2.5 = 6 × 2.5 = 15m. Example: What is the perimeter of a trapezoid having side-lengths 10 cm, 7 cm, 6 cm, and 7 cm? The perimeter is the sum 10 + 7 + 6 + 7 = 30cm.

The distance around a circle. It is equal to Pi times the diameter of the circle. Pi or is a number that is approximately 3.14159. Example: What is the circumference of a circle having a diameter of 7.9 cm, to the nearest tenth of a cm? Using an approximation of 3.14159 for, and the fact that the circumference of a circle is times the diameter of the circle, the circumference of the circle is Pi × 7.9  3.14159 × 7.9 = 24.81…cm, which equals 24.8 cm when rounded to the nearest tenth of a cm. Visit the Math League [Online Info] [|www.mathleague.com]


 * Perimeter and Area ** 

Problems
**Problem 2.1:** //Diagram of a Rectangle// What is the area of this rectangle? If you said 20 your RIGHT


 * Problem 2.4:** [[image:http://img.sparknotes.com/figures/2/2e8a313ab87d8d9656417d9ad2b59f65/problem_square1.gif]]//Diagram of a Square// What is the area of this square? If you said 49 your right


 * Problem 2.5**

//Diagram of a Square// What is the area of this square? If you said 9 your Right



Area and Perimeter. [Online Image]. []======

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 * area [online image]**[|www.grc.nasa.gov] 6/19/09