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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 Find areas of rhombi. Area of Triangles. If the triangle has the area ( A) , base ( b) , and height ( h) , then… A=1/2bh. B. h. A. C. b.

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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 • Find areas of rhombi

  3. Area of Triangles • If the triangle has the area (A) , base (b), and height (h), then… A=1/2bh B h A C b

  4. Find the area of the triangle if the base is 9 in. and the height is 5 in. A=1/2bh Example 1: B C 5 9 A

  5. Example 1: Since the base is 9 in. and the height is 5 in. your equation should read, A=1/2(5x9) Solve A=1/2(45) Multiply. A=22.5 Multiply by ½. The area of triangle ABC is 22.5 square inches. 

  6. Area of Quadrilaterals Using Δ's The area of a quadrilateral is equal to the sum of the areas of triangle FGI and triangle GHI. A (FGHI)= ½(bh) + ½(bh) g F G I H

  7. Example 2: Find the area of the quadrilateral if FH= 37 in. G 9 in. F 18 in. I H

  8. Example 2: A= ½(37x9)+ ½(37x18) Solve. A= ½(333) + ½(666) Multiply. A= 166.5 + 333 Add. A= 499.5 square inches

  9. Area of a Trapezoid If a trapezoid has an area (A), bases (b1 and b2), and height (h), then… A= ½ h (b1+b2) b2 h b1

  10. Example 3: Find the area of the trapezoid. 16 yd. 14 yd. 12 yd. 24 yd.

  11. Example 3: A= ½x12(16+24) Add. A= ½x12(40) Multiply. A= ½(480) Multiply. A= 240 square yards.

  12. Area of Rhombi If a rhombus has an area of A square units and diagonals of d1 and d2 units, then… A= ½(d1xd2) (AC is d1, BD is d2) A B d1 d2 D C

  13. Example 4: Find the area of the rhombus if ML= 20m and NP= 24m. N M L P

  14. Example 4: A= ½(20x24) Multiply. A= ½(480) Multiply. A= 240 Square meters.

  15. Find the Missing Measures Rhombus WXYZ has an area of 100 square meters. Find XZ if WY= 20 meters. X Y W Z

  16. Use the formula for the area of a rhombus and solve for D1 (XZ) A= ½(d1xd2) 100= ½(d1)(20) Substitution. 100= 10(d1) Multiply. 10=d1 Divide. XZ= 10 meters

  17. Postulate 11.1 Postulate 11.1: Congruent figures have equal areas.

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