Question

Tara and Veronica are in charge of making a banner for the volleyball game this Saturday.How much poster paper will they need for a parallelogram-shaped banner with a height 3 1/2 and base 6 1/4?

Answer 1

The answer is 21 7/8.

The quantity of the paper needed is the area of parallelogram with a height 3 1/2 and base 6 1/4. The area of a parallelogram (A) is the product of its height (h) and base (b):
A = h * b

We have:
$h = 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{3}{1} +\frac{1}{2}= \frac{3*2}{1*2}+\frac{1}{2}=\frac{6}{2}+\frac{1}{2}=\frac{7}{2} \\ \\ b = 6 \frac{1}{4} = 6 + \frac{1}{4} = \frac{6}{1} +\frac{1}{4}= \frac{6*4}{1*4}+\frac{1}{4}=\frac{24}{4}+\frac{1}{4}=\frac{25}{4}$


Thus, the area of paralleogram is:
$A = b * h = \frac{7}{2} * \frac{25}{4} = \frac{7*25}{2*4} = \frac{175}{8} = \frac{168+7}{8} = \frac{168}{8} + \frac{7}{8} = 21+ \frac{7}{8}=21\frac{7}{8}$