Question

Find the area of the polygon.

Answer 1

Answer:

  66 cm²

Step-by-step explanation:

As you know from the area formulas, the area of a triangle is equivalent to half the area of a rectangle with the same base and height. Another way to say that is the area of a triangle is equivalent to the area of a rectangle with the same base and half the height.

The triangle added to the side of the square is equivalent in area to a rectangle with the same 6 cm base (vertical dimension), and half the 10 cm height (horizontal dimension). That is, the total area of the polygon is the same as the area of one that is 6 cm high and 6+5 = 11 cm wide.

  A = LW = (6 cm)(11 cm) = 66 square centimeters

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If you want to figure the area more conventionally, it is the sum of the area of a 6 cm square and a 6×10 cm triangle:

  6² +1/2(6)(10) = 36 +30 = 66 . . . square centimeters