Question

what is the area? write your answer as a fraction or as a whole or mixed number. image of a parallelogram with height 3 ft and base 3 5/6 ft square feet submit work it out not feeling ready yet? these can help.

Explanation:

Step1: Recall the area formula for a parallelogram

The area \( A \) of a parallelogram is given by the formula \( A = base \times height \).

Step2: Identify the base and height

From the diagram, the base \( b \) is \( 3\frac{5}{6} \) feet and the height \( h \) is \( 3 \) feet.

Step3: Convert the mixed number to an improper fraction

First, convert \( 3\frac{5}{6} \) to an improper fraction. \( 3\frac{5}{6}=\frac{3\times6 + 5}{6}=\frac{18+5}{6}=\frac{23}{6} \).

Step4: Multiply the base and height

Now, multiply the base (\( \frac{23}{6} \)) and the height (\( 3 \)): \( A=\frac{23}{6}\times3 \). Simplify this: \( \frac{23\times3}{6}=\frac{69}{6} \).

Step5: Simplify the fraction

Simplify \( \frac{69}{6} \) by dividing numerator and denominator by their greatest common divisor, which is \( 3 \). \( \frac{69\div3}{6\div3}=\frac{23}{2} \). Convert \( \frac{23}{2} \) to a mixed number: \( \frac{23}{2}=11\frac{1}{2} \).

Answer:

\( 11\frac{1}{2} \)