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Directions: Find the area of the following figures. 3.

Mathematics

ScanSolve AI Answer

Answer

9840 cm29840 \text{ cm}^2

Step-by-step solution

5 steps
  1. Identify the dimensions of the trapezoid and ensure consistent units.

    The figure is a trapezoid. The parallel bases are the top and bottom sides.
    Base 1 (b1b_1) = 13 m13 \text{ m}
    Base 2 (b2b_2) = 12 cm12 \text{ cm}
    The right angle symbol indicates that the side labeled 15 cm15 \text{ cm} is perpendicular to the 12 cm12 \text{ cm} base. Therefore, the height (hh) = 15 cm15 \text{ cm}.

    To perform calculations, all units must be consistent. Convert b1b_1 from meters to centimeters:
    b1=13 m×100 cm/m=1300 cmb_1 = 13 \text{ m} \times 100 \text{ cm/m} = 1300 \text{ cm}.

    Now we have:
    b1=1300 cmb_1 = 1300 \text{ cm}
    b2=12 cmb_2 = 12 \text{ cm}
    h=15 cmh = 15 \text{ cm}

  2. Write the formula for the area of a trapezoid.

    The area AA of a trapezoid is given by the formula:

    A=12h(b1+b2)A = \frac{1}{2} h (b_1 + b_2)
  3. Substitute the values into the formula.

    A=12(15 cm)(1300 cm+12 cm)A = \frac{1}{2} (15 \text{ cm}) (1300 \text{ cm} + 12 \text{ cm})
  4. Calculate the sum of the bases.

    A=12(15 cm)(1312 cm)A = \frac{1}{2} (15 \text{ cm}) (1312 \text{ cm})
  5. Perform the multiplication to find the area.

    A=15×13122 cm2A = 15 \times \frac{1312}{2} \text{ cm}^2 A=15×656 cm2A = 15 \times 656 \text{ cm}^2 A=9840 cm2A = 9840 \text{ cm}^2

    The area of the trapezoid is 9840 cm29840 \text{ cm}^2.

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