Math

QuestionWhat fraction of Polygon B's area is Polygon A's area if B is a scaled copy of A with a scale factor of 5?

Studdy Solution

STEP 1

Assumptions1. Polygon B is a scaled copy of Polygon A with a scale factor of5. . We are asked to find the area of Polygon A as a fraction of the area of Polygon B.

STEP 2

The area of a scaled copy of a polygon is the square of the scale factor times the area of the original polygon. This can be expressed as followsAreaB=(Scalefactor)2timesAreaAArea_{B} = (Scale\, factor)^2 \\times Area_{A}

STEP 3

We can rearrange the equation to express the area of Polygon A as a fraction of the area of Polygon B.
AreaA=AreaB(Scalefactor)2Area_{A} = \frac{Area_{B}}{(Scale\, factor)^2}

STEP 4

Now, plug in the given values for the scale factor to calculate the fraction.
AreaA=AreaB()2Area_{A} = \frac{Area_{B}}{()^2}

STEP 5

Calculate the fraction.
AreaA=AreaB25Area_{A} = \frac{Area_{B}}{25}So, the area of Polygon A is1/25 of the area of Polygon B.

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