Question

what is the missing length?
3.6 mm
9 mm
area = 95.13 mm²
w = millimeters
submit

Explanation:

Step1: Recall trapezoid area formula

The area \( A \) of a trapezoid is given by \( A=\frac{(a + b)}{2}\times h \), where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height (the perpendicular distance between them). Here, \( a = 3.6\space\text{mm} \), \( b = 9\space\text{mm} \), \( A = 95.13\space\text{mm}^2 \), and \( h = w \) (the missing length we need to find).

Step2: Substitute values into the formula

Substitute the known values into the formula: \( 95.13=\frac{(3.6 + 9)}{2}\times w \)

Step3: Simplify the sum inside the fraction

First, calculate \( 3.6+9 = 12.6 \). So the equation becomes \( 95.13=\frac{12.6}{2}\times w \)

Step4: Simplify the fraction

\( \frac{12.6}{2}=6.3 \), so now we have \( 95.13 = 6.3\times w \)

Step5: Solve for \( w \)

To find \( w \), divide both sides of the equation by \( 6.3 \): \( w=\frac{95.13}{6.3} \)

Step6: Perform the division

Calculate \( \frac{95.13}{6.3}=15.1 \) (we can do this division: \( 95.13\div6.3 = 15.1 \))

Answer:

\( 15.1 \)