Question

an image of a parallelogram is shown.
what is the area of the parallelogram?

Explanation:

Step1: Convert mixed numbers to improper fractions

The formula for the area of a parallelogram is \(A = b\times h\).
The base \(b = 22\frac{1}{2}=\frac{22\times2 + 1}{2}=\frac{45}{2}\) and the height \(h=18\frac{3}{4}=\frac{18\times4+ 3}{4}=\frac{75}{4}\).

Step2: Calculate the product

\(A=\frac{45}{2}\times\frac{75}{4}=\frac{45\times75}{8}\).
\(45\times75=(40 + 5)\times75=40\times75+5\times75=3000+375 = 3375\).
So \(A=\frac{3375}{8}\).

Step3: Convert improper fraction to mixed number

\(\frac{3375}{8}=421\frac{7}{8}\) (since \(3375\div8 = 421\) with a remainder of \(7\)).

Answer:

\(421\frac{7}{8}\text{ ft}^2\) (the second option)