Areas of Rectangles and Parallelograms

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LESSON 9.1

• Areas of Rectangles and Parallelograms

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AREA OF A RECTANGLE
C-81 The area of a rectangle is given by the
formula Abh. Where b is the length of the base
and h is the height.
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AREA OF A PARALLELOGRAM
C-82 The area of a parallelogram is given by the
formula Abh. Where b is the length of the base
and h is the height of the parallelogram.
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LESSON 9.2

• Areas of Triangles, Trapezoids and Kites

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AREA OF TRIANGLES
C-83 The area of a triangle is given by the
formula . Where b is the length of the
base and h is the height (altitude) of the
triangle.
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AREA OF TRAPEZOIDS
C-84 The area of a trapezoid is given by the
formula . Where the b's are the
length of the bases and h is the height of the
trapezoid.
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AREA OF KITES
C-85 The area of a kite is given by the formula
. Where the d's are the length of the
diagonals of the triangle.
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LESSON 9.4

• Areas of Regular Polygons

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AREA OF REG. POLYGONS

• A regular n-gon has "n" sides and "n" congruent
  triangles in its interior.
• The formula for area of a regular polygon is
  derived from theses interior congruent triangles.
  
• If you know the area of these triangles will you
  know the area of the polygon?

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FORMULA TO FIND AREA OF A REGULAR POLYGON
n of sides a apothem length s sides length
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FORMULA TO FIND AREA OF A REGULAR POLYGON
C-86 The area of a regular polygon is given by
the formula , where a is the apothem
(height of interior triangle), s is the length
of each side, and n is the number of sides the
polygon has. Because the length of each side
times the number of sides is the perimeter, we
can say and .
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LESSON 9.5

• Areas of Circles

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AREA OF A CIRCLE
C-87 The area of a circle is given by the
formula , where A is the area and r is
the radius of the circle.
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LESSON 9.6

• Area of Pieces of Circles

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SECTOR OF A CIRCLE

• A sector of a circle is the region between two
  radii of a circle and the included arc.
• Formula

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AREA OF SECTOR EXAMPLE

• Find area of sector.

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SEGMENT OF A CIRCLE

• A segment of a circle is the region between a
  chord of a circle and the included arc.
• Formula

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SEGMENT OF A CIRCLE EXAMPLE

• Find the area of the segment.

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ANNULUS

• An annulus is the region between two concentric
  circles.
• Formula

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LESSON 9.7

• Surface Area

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TOTAL SURFACE AREA (TSA)

• The surface area of a solid is the sum of the
  areas of all the faces or surfaces that enclose
  the solid.
• The faces include the solid's top and bottom
  (bases) and its remaining surfaces (lateral
  surfaces or surfaces).

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TSA OF A RECTANGULAR PRISM

• Find the area of the rectangular prism.

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TSA OF A CYLINDER

• Formula
• Example

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TSA OF A PYRAMID

• The height of each triangular face is called the
  slant height.
• The slant height is usually represented by "l"
  (lowercase L).

Example
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TSA OF A CONE

• Formula
• Example