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11.2 Areas of Triangles, Trapezoids, and Rhombi

11.2 Areas of Triangles, Trapezoids, and Rhombi. Objectives. Find areas of triangles. Find areas of trapezoids and rhombi. Area of a Triangle. If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A=½ bh. Example 1.

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11.2 Areas of Triangles, Trapezoids, and Rhombi

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  1. 11.2 Areas of Triangles, Trapezoids, and Rhombi

  2. Objectives • Find areas of triangles. • Find areas of trapezoids and rhombi.

  3. Area of a Triangle • If a triangle has an area of A square units, a base of b units, and a corresponding height of h units, then A=½bh.

  4. Example 1 Find the area of quadrilateral XYZW if XZ=39, HW=20, and YG=21. The area of the quadrilateral is equal to the sum of the areas of triangle XWZ and triangle XYZ. area of XYZW= area of triangle XYZ+ area of triangle XWZ

  5. Ex. 1 continued.. =½bh₁ + ½bh₂ =½(39)(21) + ½(39)(20) =409.5 + 390 =799.5

  6. Areas of Trapezoids • If a trapezoid has an area of A square units, bases of b₁ units and b₂ units, and a height of h units, then A=½h(b₁ + b₂).

  7. Example 2 Find the area of the trapezoid. h=7, b₁=9, and b₂=11

  8. Ex. 2 continued.. = ½(7)(9+11) =½(7)(20) =½(140) =70

  9. Area of a Trapezoid on the Coordinate Plane Find the area of trapezoid TVWZ with vertices T(-3,4), V(3,4), W(6,-1), and Z(-5,-1). • Bases: Since TV and ZW are horizontal, find their length by subtracting the x-coordinates of their endpoints. • Height: Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates.

  10. Coordinates cont.. =½h(b₁ + b₂) =½(5)(6+11) =½(5)(17) =½(85) =42.5

  11. Area of a Rhombus If a rhombus has an area of A square units and diagonals of d₁ and d₂ units, then A=½d₁d₂. Ex. A=½(AC)(BD)

  12. Example 3 Find the area of the rhombus. d₁=12, d₂=6

  13. Example 3 cont.. =½(12)(6) =½(72) =36

  14. Area of a rhombus on a coordinate plane Find the area of rhombus EFGH with vertices at E(-1,3), F(2,7), G(5,3), and H(2,-1). Plan: • Find the lengths of each diagonal. • Let EG be d₁ and FH be d₂. • Subtract the x-coordinates of E and G to find that d₁ is 6. • Subtract the y-coordinates of F and H to find that d₂ is 8.

  15. Coordinates cont.. =½(6)(8) =½(48) =24

  16. Find Missing Measures Rhombus WXYZ has an area of 100 square meters. Find WY if XZ=10 meters. Use the formula for the area of a rhombus and solve for d₂. A=½d₁d₂ 100=½10x 100=5x X=20

  17. Postulate 11.1 • Congruent figures have equal areas.

  18. Assignment • Pre-AP Geometry: pg. 606 #13-22, 26, 30-35 • Geometry: umm NO.

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