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Areas of Trapezoids, Rhombuses, and Kites

Learn how to calculate the areas of trapezoids, rhombuses, and kites with step-by-step examples. Discover the formulas and theorems to solve for the area of each shape.

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Areas of Trapezoids, Rhombuses, and Kites

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  1. Areas of Trapezoids, Rhombuses, and Kites Objective: • To find the areas of trapezoids, rhombuses, and kites

  2. Example 1 Find the area of the parallelogram

  3. Bases and Heights The parallel sides of a trapezoid are the bases. The altitude is a segment connecting the bases that is perpendicular to both. The length of the altitude (the distance between the bases) is the height.

  4. Investigation 1 In this Investigation, you will discover a formula for computing the area of a trapezoid.

  5. Area of a Trapezoid Theorem The area of a trapezoid is one half the product of the height and the sum of the lengths of the bases.

  6. Example 2 Find the area of the trapezoid.

  7. Example 3 Find the area of each trapezoid.

  8. Example 4 Find the value of x.

  9. Investigation 2 The following investigation will demonstrate how to compute the area of a kite. Click on the picture to start.

  10. Area of a Kite Theorem The area of a kite is one half the product of the lengths of its diagonals.

  11. Example 5 Find the area of the kite to the nearest whole square unit.

  12. Example 6 Find the area of each kite.

  13. Example 7 Find the value of x. x 15

  14. Investigation 3 This last investigation will demonstrate an alternate method of finding the area of a rhombus.

  15. Area of a Rhombus Theorem The area of a rhombus is one half the product of the length of its diagonals.

  16. Example 8 Find the area of the rhombus.

  17. Example 9 Find the area of each rhombus.

  18. Example 10 Find the value of x. x 12

  19. Example 11 Find the area of each figure.

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