Question

1. surface area = 290 mm²

Explanation:

Step1: Recall the surface - area formula for a rectangular prism

The surface - area formula of a rectangular prism is \(S = 2(lw+lh + wh)\), where \(l = 11\) mm, \(w=x\) mm, \(h = 3\) mm, and \(S=290\) \(mm^{2}\).
Substitute the values into the formula: \(290=2(11x + 11\times3+3x)\).

Step2: Simplify the equation

First, divide both sides of the equation by 2: \(\frac{290}{2}=\frac{2(11x + 33+3x)}{2}\), which gives \(145=11x + 33+3x\).
Then, combine like terms: \(145=(11x + 3x)+33\), so \(145 = 14x+33\).

Step3: Solve for \(x\)

Subtract 33 from both sides: \(145−33=14x+33 - 33\), which results in \(112 = 14x\).
Divide both sides by 14: \(x=\frac{112}{14}\).

Answer:

\(x = 8\) mm