Answer:
The area of polygon JKLMNO is 48 square units
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the scale factor
we know that
If two figures are similar, the the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
Let
z ----> the scale factor
The scale factor of the dilation of polygon PQRSTU to polygon JKLMNO is
[tex]z=\frac{KJ}{QP}[/tex]
substitute the given values
[tex]z=\frac{4}{5}[/tex]
step 2
Find the area of polygon JKLMNO
we know that
If two figures are similar, the the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> area of polygon JKLMNO
y ----> area of polygon PQRSTU
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{4}{5}[/tex]
[tex]y=75\ units^2[/tex]
substitute
[tex](\frac{4}{5})^{2}=\frac{x}{75}[/tex]
solve for x
[tex]x=(\frac{16}{25})75=48\ units^2[/tex]
therefore
The area of polygon JKLMNO is 48 square units
