Respuesta :

To find the dimensions if a trapezoid with an area of 100 square centimeters, you will use your understanding of solving equations and the trapezoid formula to find the missing parts.

Please see the attached picture for the sketch and work in finding the missing bases and height of the trapezoid.

Ultimately, you will need 2 factors that give you 200 square centimeters.
Ver imagen Mrscomputator

Answer and step-by-step explanation:

The formula for the area of a trapezoid is

[tex]A=\frac{1}{2}(b+B)(h)[/tex]

Substituting 100 in for A,

[tex]100=\frac{1}{2}(b+B)(h)[/tex]

Cancel the 1/2 by multiplying both sides by 2:

[tex]100(2)=\frac{1}{2}(b+B)(h)(2)\\\\200=(b+B)(h)[/tex]

We want the sum of the bases multiplied by the height to be 200.

If we let the height be 10, this would make the sum of the bases 200/10 = 20.

Any two numbers that sum to 20 will work; we can use 7 for the smaller base and 13 for the larger one.

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