Question

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Answer 1

9514 1404 393

Answer:

  51 square inches

Step-by-step explanation:

This can be considered a couple of ways:

1. a 6 in × 7 in rectangle with a 6 in × 3 in triangle added on
2. a 6 in × 13 in rectangle with a 6-in high trapezoid cut from the lower right corner.

The formulas for areas of these figures are ...

  A = 1/2bh . . . . area of triangle with base b and height h

  A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h

  A = bh . . . . . . . area of a rectangle with base b and height h

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1. rectangle area = (6 in)(7 in) = 42 in²

  triangle area = 1/2(6 in)(3 in) = 9 in²

Total area of the figure:

  42 in² +9 in² = 51 in²

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2. rectangle area = (6 in)(13 in) = 78 in²

  trapezoid area = 1/2(6 in + 3 in)(6 in) = 27 in²

Total area of the figure:

  78 in² -27 in² = 51 in²

The area of the composite shape is 51 square inches.