Question

Use the image to answer the question.

A horizontally aligned rectangle is shown as 10 meters long and 6 meters wide. A rectangular area is removed from the bottom right corner, with the remaining length as 8 meters and remaining width as 4 meters. Right angle marks are shown in the five corners of the composite shape.

Rebekah designs a playing field for a new sport. The playing field is pictured. What is the area of the playing field?

(1 point)
Responses

58 square meters
58 square meters

56 square meters
56 square meters

32 square meters
32 square meters

60 square meters

Answer 1

To find the area of the playing field, we need to calculate the area of the original rectangle and then subtract the area of the rectangular section that was removed.

1. **Calculate the area of the original rectangle:**
\[
\text{Area of original rectangle} = \text{length} \times \text{width} = 10 \, \text{m} \times 6 \, \text{m} = 60 \, \text{square meters}
\]

2. **Calculate the area of the removed rectangle:**
The remaining length and width given for the playing field are 8 meters and 4 meters, respectively. Therefore, the dimensions of the area that was removed are:
- Removed length = 10 m - 8 m = 2 m
- Removed width = 6 m - 4 m = 2 m

Now calculate the area of the removed rectangle:
\[
\text{Area of removed rectangle} = \text{length} \times \text{width} = 2 \, \text{m} \times 2 \, \text{m} = 4 \, \text{square meters}
\]

3. **Calculate the area of the playing field:**
\[
\text{Area of playing field} = \text{Area of original rectangle} - \text{Area of removed rectangle} = 60 \, \text{square meters} - 4 \, \text{square meters} = 56 \, \text{square meters}
\]

So, the area of the playing field is **56 square meters**.