Question

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

image of parallelogram pqrs with side lengths: rs = 32 in, sp = 29.6 in, rq = 29.6 in, qp = 32 in, and height from s to qp is 24.4 in (right angle symbol at the foot of the height on qp).

Explanation:

Step1: Recall the formula for the area of a parallelogram

The area \( A \) of a parallelogram is given by the formula \( A = base \times height \), where the base is the length of one of the sides, and the height is the perpendicular distance from that side to the opposite side.

Step2: Identify the base and the corresponding height

From the diagram, we can see that the base \( b \) of the parallelogram can be taken as \( 32 \) inches, and the corresponding height \( h \) (the perpendicular distance) is \( 24.4 \) inches.

Step3: Calculate the area

Using the formula \( A = base \times height \), we substitute the values of the base and height:
\[
A = 32 \times 24.4
\]
\[
A = 780.8
\]

Answer:

The area of parallelogram \( PQRS \) is \( 780.8 \) square inches.