3. Carlos cuts blue parallelograms and larger red parallelograms to use in his decoupage. He realizes the parallelograms are similar. What is the Round to the nearest tenth area of the larger, red parallelogram? Round to the nearest tenth

Answer:The area of the larger parallelogram is [tex]180\ cm^{2}[/tex]Step-by-step explanation:step 1Find the scale factorwe know thatIf two figures are similar, then the ratio of its corresponding sides is the scale factor Let z------> the scale factor[tex]z=\frac{24}{16}=1.5[/tex]step 2Find the area of the larger parallelogramwe know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLet z------> the scale factorx------> the area of the larger parallelogramy-------> the area of the smaller parallelogramso[tex]z^{2}=\frac{x}{y}[/tex]we have[tex]z=1.5[/tex][tex]y=80\ cm^{2}[/tex]substitute the values[tex]1.5^{2}=\frac{x}{80}[/tex][tex]x=80*(1.5^{2})=180\ cm^{2}[/tex]