Question

a cube has a lateral area of 676 square feet. what is the side length of the cube? 4.3 feet 6.5 feet 10.6 feet 13 feet

Explanation:

Step1: Recall the formula for the lateral area of a cube

The lateral area \(L\) of a cube with side length \(s\) is \(L = 4s^{2}\).

Step2: Substitute the given lateral area into the formula

Given \(L=676\), so \(4s^{2}=676\).

Step3: Solve for \(s^{2}\)

Divide both sides by \(4\): \(s^{2}=\frac{676}{4}=169\).

Step4: Solve for \(s\)

Take the square root of both sides: \(s = \sqrt{169}=13\).

Answer:

13 feet