Practice Problems
\(\textbf{1)}\) The two figures are similar. The Area of the larger figure is \(558\). Find the area of the smaller figure.
The area of the smaller figure is \( 248 \)
\(k=\frac{18}{12}=1.5\)
\(k^2=2.25\)
\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)
\(\displaystyle\frac{558}{x}=\frac{2.25}{1}\)
\(2.25\cdot x=558\)
\(x=248\)
The area of the smaller figure is \( 248 \)
\(\textbf{2)}\) The two figures are similar. The area of the larger figure is \(16\). Find the area of the smaller figure.
The area of the smaller figure is \( 4 \)
\(k=\frac{6}{3}=2\)
\(k^2=4\)
\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)
\(\displaystyle\frac{16}{x}=\frac{4}{1}\)
\(4\cdot x=16\)
\(x=4\)
The area of the smaller figure is \( 4 \)
\(\textbf{3)}\) The two figures are similar. The area of the smaller figure is \(135\). Find the area of the larger figure.
The area of the larger figure is \( 375 \)
\(k=\frac{20}{12}=\frac{5}{3}\)
\(k^2=\frac{25}{9}\)
\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)
\(\displaystyle\frac{x}{135}=\frac{25}{9}\)
\(9\cdot x=135 \cdot 25\)
\(x=375\)
The area of the larger figure is \( 375 \)
\(\textbf{4)}\) The two figures are similar. The area of the smaller figure is \(2385\). Find the area of the larger figure.
The area of the larger figure is \( 4240 \)
\(\textbf{5)}\) The two figures are similar. The area of the larger figure is \(900\). Find the area of the smaller figure.
The area of the smaller figure is \( 400 \)
\(\textbf{6)}\) The two figures are similar. The area of the smaller figure is \(42\). Find the area of the larger figure.
The area of the larger figure is \( 168 \)
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