Answer:
[tex]\boxed{\text{10 units}^{2}}[/tex]
Step-by-step explanation:
The scale factor (C) is the ratio of corresponding parts of the two polygons.
The ratio of the areas is the square of the scale factor.
[tex]\dfrac{A_{\text{D}}}{ A_{\text{C}}} = C^{2}\\\\\dfrac{ A_{\text{D}}}{40} = \left (\dfrac{1}{2}\right)^{2}\\\\\dfrac{ A_{\text{D}}}{40}= \dfrac{1}{4}\\\\A_{\text{D}}= \dfrac{40}{4 }= \textbf{10}\\\\\text{The area of the smaller polygon is $\boxed{\textbf{10 units}^{\mathbf{2}}}$}[/tex]
The area of polygon D is 10 square units given that a polygon has an area of 40 square units and Kennan drew a scale version of polygon C using a scale factor of 1/2 and labeled it polygon D. This can be obtained by using area ratio and scale factor relation.
The ratio of areas is equal to square of scale factor.
[tex]\frac{A_{D} }{A_{C} }=C^{2}[/tex], where C is the scale factor, [tex]A_{D}[/tex] is the area of polygon D, [tex]A_{C}[/tex] is the area of polygon C.
Given that, area of polygon C = 40 square units
scale factor = 1/2
Putting in the relation, [tex]\frac{A_{D} }{40} =(\frac{1}{2} )^{2}[/tex]
[tex]\frac{A_{D} }{40} =\frac{1}{4}[/tex]
[tex]A_{D} =\frac{40}{4}=10[/tex]
Hence the area of polygon D is 10 square units given that a polygon has an area of 40 square units and Kennan drew a scale version of polygon C using a scale factor of 1/2 and labeled it polygon D.
Learn more about scale factor here:
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