Question

an image of a parallelogram is shown. what is the area of the parallelogram? 444\frac{3}{8}ft^{2} 421\frac{7}{8}ft^{2} 412\frac{1}{2}ft^{2} 405\frac{1}{2}ft^{2}

Explanation:

Step1: Convert mixed numbers to improper fractions

The formula for the area of a parallelogram is \(A = b\times h\).
\(18\frac{3}{4}=\frac{18\times4 + 3}{4}=\frac{72+3}{4}=\frac{75}{4}\)
\(22\frac{1}{2}=\frac{22\times2+1}{2}=\frac{44 + 1}{2}=\frac{45}{2}\)

Step2: Calculate the area

\(A=\frac{75}{4}\times\frac{45}{2}=\frac{75\times45}{4\times2}=\frac{3375}{8}\)
\(\frac{3375}{8}=421\frac{7}{8}\) (because \(3375\div8 = 421\) with a remainder of \(7\))

Answer:

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