Question

what is the missing length?
area of shaded region ( = 21mm^{2})( y=)millimeters

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle is \( A=\frac{1}{2}\times base\times height \). Here, the base is \( 6\) mm and the height is \( y\), and the area \( A = 21\) \(mm^{2}\).

Step2: Substitute the values into the formula

Substitute \(A = 21\), \(base=6\) into \(A=\frac{1}{2}\times base\times height\). We get \(21=\frac{1}{2}\times6\times y\).
First, simplify the right - hand side: \(\frac{1}{2}\times6\times y=3y\). So the equation becomes \(3y = 21\).

Step3: Solve for \(y\)

Divide both sides of the equation \(3y = 21\) by \(3\). Using the formula \(y=\frac{21}{3}\).

Answer:

\(7\)