## Lesson 9: Areas (II)

May 9, 2011**4.Perimeter of a circumference and length of a an arc**

The **length of a circumference of radius r and diameter **

**d = 2r**is L =2πr or L=πd.The **length of an arc** *of aº is L _{arc} = 2πr · aº/360º. *

You don’t need to learn this formula because it is easy to find out by applying a rule of three direct:

2πr ———- 360º

L_{arc ———– aº Larc = 2πr · aº/360º }

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The following table revises the formulae we studied in this lesson.

**5.Area of Plane Shapes**

Square AreaA = a^{2}a = length of side |
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Parallelogram AreaA = b · h b = base h = vertical height |
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Circle AreaA = πr^{2}Circumference=2πr r = radius |
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Sector circle AreaA = (πr^{2} · θ) /360ºr = radius θº = angle in degrees |

**6.Area of a Circular Ring or Annulus**

A circular ring (**annulus or crown**) is plane figure bounded by the circumference of two concentric circles of two different radii. The **area of a circular ring** is found by subtraction the area of small circle from that of the large circle.

A_{r }= π(R^{2} – r^{2})

** 7.Composite Figures**

**Composite figures (or shapes)** are figures (or shapes) that can be divided into more than one of the basic figures. Their area can be calculated by adding (or subtracting) the areas of the figures they are divided into.

One example would be the annulus.

Here you are some links to practice with areas and revise perimeters. The level is elemental.

1. Perimeter

2.Area

3. Area and perimeter: word problems

5. Circles: calculate area, circumference, radius, and diameter

**8. Sum of the interior angles of a polygon**

The **sum of the interior angles of a n-sided polygon** is (n-2) · 180º.

In this case, we have an hexagon so the sum of the interior angles is (6-2) · 180º.

In a **regular n-sided polygon** all the interior angles are equal so **each interior angle** measures (n-2) · 180º/n.

Here you are a video on calculating the sum of the interior angles of 17-sided polygon.

**9. Central angle of a regular n-sided polygon**

The **central angle of a regular n-sided polygon** measures 360º/n

In this case we have a pentagon so its central angle is 360º/5 =72º

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