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LESSON 9.1

LESSON 9.1. Areas of Rectangles and Parallelograms. AREA OF A RECTANGLE. C-81 : The area of a rectangle is given by the formula A=bh. Where b is the length of the base and h is the height. AREA OF A PARALLELOGRAM.

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LESSON 9.1

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  1. LESSON 9.1 • Areas of Rectangles and Parallelograms

  2. AREA OF A RECTANGLE C-81: The area of a rectangle is given by the formula A=bh. Where b is the length of the base and h is the height.

  3. AREA OF A PARALLELOGRAM C-82: The area of a parallelogram is given by the formula A=bh. Where b is the length of the base and h is the height of the parallelogram.

  4. LESSON 9.2 • Areas of Triangles, Trapezoids and Kites

  5. 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.

  6. 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.

  7. 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.

  8. LESSON 9.4 • Areas of Regular Polygons

  9. 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?

  10. FORMULA TO FIND AREA OF A REGULAR POLYGON n= # of sides a = apothem length s = sides length

  11. 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 .

  12. LESSON 9.5 • Areas of Circles

  13. 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.

  14. LESSON 9.6 • Area of Pieces of Circles

  15. SECTOR OF A CIRCLE • A sector of a circle is the region between two radii of a circle and the included arc. • Formula:

  16. AREA OF SECTOR EXAMPLE • Find area of sector.

  17. SEGMENT OF A CIRCLE • A segment of a circle is the region between a chord of a circle and the included arc. • Formula:

  18. SEGMENT OF A CIRCLE EXAMPLE • Find the area of the segment.

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

  20. LESSON 9.7 • Surface Area

  21. 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).

  22. TSA OF A RECTANGULAR PRISM • Find the area of the rectangular prism.

  23. TSA OF A CYLINDER • Formula: • Example:

  24. 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:

  25. TSA OF A CONE • Formula: • Example:

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