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Practice Problems

\(\textbf{1)}\) The two figures are similar. The Area of the larger figure is \(558\). Find the area of the smaller figure.

Show Area

The area of the smaller figure is \( 248 \)

Show Work

\(k=\frac{18}{12}=1.5\)

\(k^2=2.25\)

\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)

\(\displaystyle\frac{558}{x}=\frac{2.25}{1}\)

\(2.25\cdot x=558\)

\(x=248\)

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.

Show Area

The area of the smaller figure is \( 4 \)

Show Work

\(k=\frac{6}{3}=2\)

\(k^2=4\)

\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)

\(\displaystyle\frac{16}{x}=\frac{4}{1}\)

\(4\cdot x=16\)

\(x=4\)

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.

Show Area

The area of the larger figure is \( 375 \)

Show Work

\(k=\frac{20}{12}=\frac{5}{3}\)

\(k^2=\frac{25}{9}\)

\(\displaystyle\frac{\text{Area Large Figure}}{\text{Area Small Figure}}=k^2\)

\(\displaystyle\frac{x}{135}=\frac{25}{9}\)

\(9\cdot x=135 \cdot 25\)

\(x=375\)

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.

Show Area

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.

Show Area

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.

Show Area

The area of the larger figure is \( 168 \)

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