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Areas of Trapezoids, Rhombi & Kites Areas of Circles & Sectors

Areas of Trapezoids, Rhombi & Kites Areas of Circles & Sectors. Notes 11 – Sections 11.2 & 11.3. Essential Learnings. Students will understand and be able to find the perimeter and areas of trapezoids, rhombi, and kites.

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Areas of Trapezoids, Rhombi & Kites Areas of Circles & Sectors

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  1. Areas of Trapezoids, Rhombi & KitesAreas of Circles & Sectors Notes 11 – Sections 11.2 & 11.3

  2. Essential Learnings • Students will understand and be able to find the perimeter and areas of trapezoids, rhombi, and kites. • Students will understand and be able to find the areas circles and sectors of circles.

  3. Area of a Trapezoid The area A of a trapezoid is one half the product of the height h and the sum of its bases b1 and b2. A = ½ (b1 + b2)h base 1 height base 2

  4. Area of a Rhombus or Kite The area A of a rhombus or kite is one half the product of the lengths of its diagonals, d1and d2. A = ½ d1d2 d1 d1 d2 d2

  5. Example 1 (8-9) Find the area of the trapezoid. 18 m 16 m 32 m

  6. Example 2 (10-12) Find the area of the kite. 5 m 10 m 6 m

  7. Example 3 (10-12) Find the area of the rhombus. 5 ft 9 ft

  8. Example 4 (18-21) One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 square meters, what are the lengths of the diagonals?

  9. Example 5 (18-21) A trapezoid had a height of 40 inches, a base of 15 inches and an area of 2400 square inches. What is the length of the other base?

  10. Example 6 (26-27) Find the area of parallelogram RVHS with R (-1, 8), V (7, 8), H (0, 3), and S (-8, 3)

  11. Circles and Sectors

  12. Area of a Circle The area A of a circle is equal to π times the square of the radius r.

  13. Example 1 (8) Find the area of a circle with a radius of 5 yards.

  14. Example 2 (10-14) The area of a circle is 26 square centimeters. Find the diameter.

  15. Vocabulary Central angle – an angle that intersects a circle in two points and has its vertex at the center of the circle. A sector of a circle is a region of a circle bounded by a central angle and its intercepted arc. Intercepted Arc

  16. Area of a Sector The ratio of the area A of a sector to the area of the whole circle, πr2, is equal to the ratio of the degree measure of the intercepted arc x.

  17. Example 3 (18-22) Find the area of the shaded sector. Round to the nearest tenth. 88 7.5 cm

  18. Example 4 (18-22) Find the area of the shaded sector. Round to the nearest tenth. 51 r = 2 m

  19. Example 5 (32-35) Find the area of the shaded sector if the side of the square is 15 ft. Round to the nearest tenth.

  20. Example 6 (40) Find the area of the shaded region. 20 in.

  21. Assignment Pages 777: 8-13, 17-21, 26, 27, 48-52 Page 785: 8–22 even, 25, 27–30, 32–35, 40, 42 Mastery Assignment – Friday Due Wednesday

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