Question

find the area of parallelogram opqr. round your answer to the nearest tenth if necessary.
(image of parallelogram opqr with sides: op = 24 in, pq = 20.4 in, qr = 24 in, ro = 20.4 in, and a height from r to op of 19.2 in, right angle marked at the foot of the height on op)

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 \( 24 \) inches. The height corresponding to this base (the perpendicular distance between the two sides of length \( 24 \) inches) is \( 19.2 \) inches (since the right angle is marked, indicating the height relative to the base of \( 24 \) inches).

Step3: Calculate the area

Using the formula \( A = base \times height \), substitute the values of base (\( 24 \) in) and height (\( 19.2 \) in):
\[
A = 24 \times 19.2
\]
\[
A = 460.8
\]

Answer:

The area of parallelogram \( OPQR \) is \( 460.8 \) square inches.