Question

find the area of parallelogram opqr. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Recall the formula for the area of a parallelogram

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

Step2: Identify the base and the corresponding height

From the diagram, we can take the base as \( 13.5 \) inches. The height corresponding to this base (the perpendicular distance between the sides of length \( 13.5 \) inches) is given as \( 11.6 \) inches (since the triangle formed with the side of length \( 10 \) inches is a right triangle, and \( 11.6 \) inches is the height relative to the base of \( 13.5 \) inches).

Step3: Calculate the area

Using the formula \( A = base \times height \), we substitute the values:
\( A = 13.5 \times 11.6 \)
First, calculate \( 13.5 \times 11.6 \):
\( 13.5 \times 11.6 = 13.5 \times (10 + 1.6) = 13.5 \times 10 + 13.5 \times 1.6 = 135 + 21.6 = 156.6 \)

Answer:

The area of parallelogram \( OPQR \) is \( 156.6 \) square inches.