QuestionPolygon $C$ has an area of 40. If Polygon $D$ is a scaled version with a scale factor of $\frac{1}{2}$ , find its area.

Studdy Solution

STEP 1

Assumptions1. The area of Polygon C is40 square units. . The scale factor used by Kennan to draw Polygon D is $\frac{1}{}$ .
3. The area of a scaled polygon is the square of the scale factor times the original area.

STEP 2

First, we need to find the area of Polygon D. We can do this by multiplying the area of Polygon C by the square of the scale factor.
$Area_{} = Area_{C} \\times (Scale\, factor)^2$

STEP 3

Now, plug in the given values for the area of Polygon C and the scale factor to calculate the area of Polygon D.
$Area_{} =40 \\times \left(\frac{1}{2}\right)^2$

STEP 4

Calculate the square of the scale factor.
$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ $Area_{} =40 \\times \frac{1}{4}$

STEP 5

Calculate the area of Polygon D.
$Area_{} =40 \\times \frac{1}{4} =10\, square\, units$ The area of Polygon D is10 square units.

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QuestionPolygon $C$ has an area of 40. If Polygon $D$ is a scaled version with a scale factor of $\frac{1}{2}$ , find its area.

Studdy Solution

STEP 1

Assumptions1. The area of Polygon C is40 square units. . The scale factor used by Kennan to draw Polygon D is $\frac{1}{}$ .
3. The area of a scaled polygon is the square of the scale factor times the original area.

STEP 2

First, we need to find the area of Polygon D. We can do this by multiplying the area of Polygon C by the square of the scale factor.
$Area_{} = Area_{C} \\times (Scale\, factor)^2$

STEP 3

Now, plug in the given values for the area of Polygon C and the scale factor to calculate the area of Polygon D.
$Area_{} =40 \\times \left(\frac{1}{2}\right)^2$

STEP 4

Calculate the square of the scale factor.
$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ $Area_{} =40 \\times \frac{1}{4}$

STEP 5

Calculate the area of Polygon D.
$Area_{} =40 \\times \frac{1}{4} =10\, square\, units$ The area of Polygon D is10 square units.

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QuestionPolygon CCC has an area of 40. If Polygon DDD is a scaled version with a scale factor of 12\frac{1}{2}21​, find its area.

Studdy Solution

STEP 1

Assumptions1. The area of Polygon C is40 square units. . The scale factor used by Kennan to draw Polygon D is 1\frac{1}{}1​.3. The area of a scaled polygon is the square of the scale factor times the original area.

STEP 2

First, we need to find the area of Polygon D. We can do this by multiplying the area of Polygon C by the square of the scale factor.Area=AreaCtimes(Scale factor)2Area_{} = Area_{C} \\times (Scale\, factor)^2Area​=AreaC​times(Scalefactor)2

STEP 3

Now, plug in the given values for the area of Polygon C and the scale factor to calculate the area of Polygon D.Area=40times(12)2Area_{} =40 \\times \left(\frac{1}{2}\right)^2Area​=40times(21​)2

STEP 4

Calculate the square of the scale factor.(12)2=14\left(\frac{1}{2}\right)^2 = \frac{1}{4}(21​)2=41​Area=40times14Area_{} =40 \\times \frac{1}{4}Area​=40times41​

STEP 5

Calculate the area of Polygon D.Area=40times14=10 square unitsArea_{} =40 \\times \frac{1}{4} =10\, square\, unitsArea​=40times41​=10squareunitsThe area of Polygon D is10 square units.

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QuestionPolygon $C$ has an area of 40. If Polygon $D$ is a scaled version with a scale factor of $\frac{1}{2}$ , find its area.

Assumptions1. The area of Polygon C is40 square units. . The scale factor used by Kennan to draw Polygon D is $\frac{1}{}$ .
3. The area of a scaled polygon is the square of the scale factor times the original area.

First, we need to find the area of Polygon D. We can do this by multiplying the area of Polygon C by the square of the scale factor.
$Area_{} = Area_{C} \\times (Scale\, factor)^2$

Now, plug in the given values for the area of Polygon C and the scale factor to calculate the area of Polygon D.
$Area_{} =40 \\times \left(\frac{1}{2}\right)^2$

Calculate the square of the scale factor.
$\left(\frac{1}{2}\right)^2 = \frac{1}{4}$ $Area_{} =40 \\times \frac{1}{4}$

Calculate the area of Polygon D.
$Area_{} =40 \\times \frac{1}{4} =10\, square\, units$ The area of Polygon D is10 square units.