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11.2 Areas of Triangles, Trapezoids, and Rhombi

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Objectives Find areas of triangles Find areas of trapezoids Find areas of rhombi

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Area of Triangles If the triangle has the area of A square units, a base of b units, and a height of h units, then… A=1/2bh A B C b h

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

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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.

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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) F g G I H

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

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

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

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

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

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Example 4: Area of a trapezoid on the coordinate plane. Since TV and ZW are horizontal, find their length by subtracting the x-coordinates from their endpoints. TV ZW (-3,4)(3,4) (-5,-1)(6,-1)

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Example 4: TV= |-3-3| TV= |-6| TV= 6 ZW= |-5-6| ZW= |-11| ZW= 11 Because the bases are horizontal segments, the distance between them can be measured on a vertical line. That is, subtract the y-coordinates. H= |4-(-1)| H= |5| H= 5

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Example 4: Now that you have the height and bases, you can solve for the area. A= ½h(b1+ b2) A= ½(5)(6+11) Substitution. A= ½(5)(17) Addition. A= ½(85) Multiply. A= 42.5 square units.

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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 D C d1 d2

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Example 5: Find the area of the rhombus if ML= 20m and NP= 24m. M L N P

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Example 5: A= ½(20x24) Multiply. A= ½(480) Multiply. A= 240 Square meters.

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Rhombus on Coordinate Plane To find the area of a rhombus on the coordinate plane, you must know the diagonals. To find the diagonals...subtract the x-coordinates to find d1, and subtract the y-coordinates to find d2.

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Example 6: Find the area of a rhombus with the points E(-1,3), F(2,7), G(5,3), and H(2,-1) F (2,7) G (5,3) H (2,-1) E (-1,3)

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Let EG be d1 and FH be d2 Subtract the x- coordinates of E and G to find d1 d1= |-1-5| d1= |-6| d1= 6 Subtract the y- coordinates of F and H to find d2 d2= |7-(-1)| d2= |8| d2= 8 F (2,7) G (5,3) H (2, -1) E (-1,3) d1 d2

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Now that you have D1 and D2, solve. A= ½(d1xd2) A= ½(6x8) Multiply. A= ½(48) Multiply. A= 24 sq. units.

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

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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

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Postulate 11.1 Postulate 11.1: Congruent figures have equal areas.

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Assignment: Pre-AP Pg. 606 #13-21, 22-28 evens, 30-35 Geometry Pg. 606 #13 – 21, 30 - 35

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