Question

write an equation for the area, a, of the parallelogram shown.
a = 3 • \frac{2}{3}
now find the area of the parallelogram.
a = \square ft²

Explanation:

Part 1: Write the equation for the area of the parallelogram

Step 1: Recall the formula for the area of a parallelogram

The formula for the area \( A \) of a parallelogram is \( A=\text{base} \times \text{height} \).

Step 2: Identify the base and height from the diagram

From the diagram, the base of the parallelogram is \( 3 \) ft and the height is \( \frac{2}{3} \) ft.

Step 3: Substitute the base and height into the formula

Substituting the values of base and height into the formula \( A = \text{base} \times \text{height} \), we get \( A=3\times\frac{2}{3} \).

Part 2: Find the area of the parallelogram

Step 1: Multiply the base and the height

We have the equation \( A = 3\times\frac{2}{3} \). When we multiply \( 3 \) (which can be written as \( \frac{3}{1} \)) by \( \frac{2}{3} \), we use the rule of multiplying fractions: \( \frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d} \). So, \( \frac{3}{1}\times\frac{2}{3}=\frac{3\times2}{1\times3} \).

Step 2: Simplify the fraction

Simplifying \( \frac{3\times2}{1\times3} \), the \( 3 \) in the numerator and the \( 3 \) in the denominator cancel out, leaving us with \( \frac{2}{1}=2 \).

Answer:

(for the area):
\( 2 \)