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Chapter 11 Length and Area

Chapter 11 Length and Area. 11.1 Areas of Triangles and Parallelograms. Area of a square = s 2 Area of a rectangle = bh Area of a parallelogram = bh Area of a triangle = bh 2. Important Information. If two polygons are congruent, then they have the same area.

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Chapter 11 Length and Area

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  1. Chapter 11Length and Area

  2. 11.1 Areas of Triangles and Parallelograms • Area of a square = s2 • Area of a rectangle = bh • Area of a parallelogram = bh • Area of a triangle = bh 2

  3. Important Information • If two polygons are congruent, then they have the same area. • The area of a region is the sum of the areas of its non-overlapping parts.

  4. 11.2 Areas of Trapezoids, Rhombuses, and Kites

  5. Formulas • Area of a trapezoid = h(b1 + b2) 2 • Area of a rhombus = d1 d2 2

  6. More Formulas • Area of a kite = d1 d2 2

  7. Examples • Find the area of RSTU. • Find the area of the polygon RSTWUV.

  8. Example • One diagonal of a kite is 1/3 as long as the other. The area of the kite is 0.24m2. What are the lengths of the diagonals?

  9. 11.3 Perimeter and Area of Similar Figures • If two polygons are similar with the lengths of corresponding sides in the ratio a:b, then the ratio of their areas is a2:b2.

  10. Example • ABCD is similar to RSTU. • Find the ratio of the perimeters. • Find the ratio of the areas.

  11. Example You are painting 2 wall in an office complex that are similar in shape- both rectangles. One wall has a side length of 10ft. The corresponding side of the other wall is 14ft. You need 7 quarts to paint the larger wall. How many quart do you need for the smaller wall?

  12. Example • The Pentagon in Washington DC is a regular pentagon with side lengths of 900ft. The area is 1,400,000ft2. The perimeter of a scale model of the building is 30yds. What is the area of the scale model?

  13. 11.4 Circumference and Arc length • Circumference – the distance around the circle

  14. Arc length- a portion of the circumference of a circle

  15. Find the length of AB • 1. 2.

  16. Find the indicated measures.

  17. 11.5 Area of Circles and Sectors • Area of a circle A = πr2 • Sector of a circle- region bounded by 2 radii of the circle and the intercepted arc. • Sector APB = m AB πr2 360o

  18. Example • Find the area of the sectors formed by <HJK.

  19. Example • Find the area between the large outer circle and the two smaller circles.

  20. 11.6 Areas of Regular Polygons • The center of a polygon and the radius of a polygon are the center and radius of its circumscribed circle. • Apothem of a polygon- distance from center to any side of a polygon • Central Angle of a regular polygon- the angle formed by 2 radii drawn to consecutive vertices of the polygon

  21. Vocabulary • Apothem • Radius • Central Angle

  22. Formula • Area of a regular polygon A =

  23. Examples • For a regular octagon inscribed in circle C, find the following: • m<RCY = • m<RCZ = • M<ZYC =

  24. Example • What is the area of a regular hexagon with a side length of 8 inches?

  25. Example • What is the area of a regular decagon inscribed in a circle with a radius of 8mm?

  26. 11.7 Using Geometric Probability • Probability (of an event) - P(A)- a measure of the likelihood that an event will occur. • Geometric probability is a ratio that involves a geometric measure like length or area.

  27. Example • Find the probability that a point chosen at random on AE is on CD. A B C D E -4 -3 -2 -1 0 1 2 3 4 5

  28. Example • A dart game uses targets with concentric circles of radii 5,8, and 12 inches. What is the probability the dart will earn 20 points?

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