Question

find the area of rectangle cdef. round your answer to the nearest tenth if necessary.

image of rectangle cdef with sides labeled: fe = 17.1 in, ed = 7.6 in, dc = 17.1 in, cf = 7.6 in, and right angles at e, d, c, f

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \).

Step2: Identify the length and width from the diagram

From the diagram, the length of the rectangle \( CDEF \) is \( 17.1 \) inches and the width is \( 7.6 \) inches.

Step3: Calculate the area

Substitute the values of length and width into the formula:
\( A = 17.1 \times 7.6 \)
First, multiply \( 171 \times 76 \) (ignoring the decimals for now):
\( 171 \times 76 = 171 \times (70 + 6) = 171 \times 70 + 171 \times 6 = 11970 + 1026 = 12996 \)
Now, count the number of decimal places in the original numbers. \( 17.1 \) has 1 decimal place and \( 7.6 \) has 1 decimal place, so the total number of decimal places is \( 1 + 1 = 2 \).
So, we place the decimal point in \( 12996 \) two places from the right: \( 129.96 \).

Answer:

The area of rectangle \( CDEF \) is \( 129.96 \) square inches. If we round to the nearest tenth, it is \( 130.0 \) square inches. But since \( 129.96 \) is already precise to the hundredth, and the question says to round to the nearest tenth if necessary, the area is \( 129.96 \) (or \( 130.0 \) when rounded to the nearest tenth). However, the exact value from the multiplication is \( 129.96 \).