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11.1 Areas of rectangles

11.1 Areas of rectangles. Postulates. The area of a square is the square of the length of a side. (A = s 2 ) If two figures are congruent, then they have the same area. s. s. Postulates. The area of a region is the sum of the areas of its non-overlapping parts. D. B. C. A. I. II.

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11.1 Areas of rectangles

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  1. 11.1 Areas of rectangles

  2. Postulates • The area of a square is the square of the length of a side. (A = s2) • If two figures are congruent, then they have the same area. s s

  3. Postulates • The area of a region is the sum of the areas of its non-overlapping parts. D B C A I II III E G F E

  4. Altitude • To a base, is any segment perpendicular to the line containing the base from any point on the opposite side.

  5. Theorem • The area of a rectangle equals the product of its base and height. • A=bh

  6. 11.2 Areas of Parallelograms, Triangles, and Rhombuses

  7. Theorem • The area of a parallelogram equals the product of a base and the height to that base. (A=bh) 12 5

  8. 31 12 45°

  9. Theorem • The area of a triangle equals half the product of a base and the height to that base ( A = ½ bh) 9 9 h 11

  10. Theorem • The area of a rhombus equals half the product of its diagonals.

  11. 431 WE 1-20, 27

  12. 11-3 Areas of Trapezoids

  13. Theorem • The area of a trapezoid equals half the product of the height and the sum of the bases. • A = ½ h(B1+B2)

  14. B1 h h B2

  15. 14 12 17

  16. This is not isosceles 8 11 7 13

  17. 11-4 Areas of Regular Polygons

  18. Definitions • Center of a regular polygon  the center of the circumscribed circle. • Radius of a regular polygon  the distance from the center to a vertex. All radii of a figure are congruent. • Central angle of a regular polygon  an angle formed by two radii drawn to consecutive vertices. All central angles are congruent. • Apothem of a regular polygon  the perpendicular distance from the center of the polygon to a side. Every apothem of a figure is congruent

  19. Theorem • The area of a regular polygon is equal to half the product of the apothem and the perimeter. • A= ½ aP • Apothems are going to be found using special right triangles, and sine, cosine, tangent functions.

  20. Find the area of a regular pentagon with perimeter of 40 centimeters.

  21. Find the area of a regular octagon with a perimeter of 72 inches.

  22. Find the area of a regular hexagon with apothem of 9.

  23. Find the area of a regular polygon with 11 sides inscribed in a circle with a radius of 12.

  24. WORKSHEETHw. Pg. 437 WE 10-14Hw. Pg. 442 CE 2-4, 6-8 WE 2-8 (ev) 13-16

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