1. The figure below is a square what is its area. \( (2 k+24) \mathrm{cm} \) \( (4 k+8) \mathrm{cm} \)

To find the area of the square, we need to know the length of one side of the square. Given that the figure is a square, all sides are equal in length. Let's denote the length of one side of the square as \( x \) cm. The area of a square is given by the formula: \[ \text{Area} = x^2 \] We are given two expressions for the length of one side of the square: 1. \( 2k + 24 \) cm 2. \( 4k + 8 \) cm Since the length of one side of the square is the same in both expressions, we can set the two expressions equal to each other: \[ 2k + 24 = 4k + 8 \] Now, we can solve for \( k \) to find the length of one side of the square. Solve the equation by following steps: - step0: Solve for \(k\): \(2k+24=4k+8\) - step1: Move the variable to the left side: \(2k+24-4k=8\) - step2: Subtract the terms: \(-2k+24=8\) - step3: Move the constant to the right side: \(-2k=8-24\) - step4: Subtract the numbers: \(-2k=-16\) - step5: Change the signs: \(2k=16\) - step6: Divide both sides: \(\frac{2k}{2}=\frac{16}{2}\) - step7: Divide the numbers: \(k=8\) The value of \( k \) is 8. Now, we can substitute the value of \( k \) back into one of the expressions for the length of one side of the square to find the length of one side of the square. Substituting \( k = 8 \) into the expression \( 2k + 24 \): \[ 2(8) + 24 = 16 + 24 = 40 \] Therefore, the length of one side of the square is 40 cm. Now, we can find the area of the square by squaring the length of one side: \[ \text{Area} = 40^2 = 1600 \, \text{cm}^2 \] So, the area of the square is 1600 cm².