Select The Correct Answer.Sides Of Three Square Rooms Measure 14 Feet Each, And Sides Of Two Square Rooms Measure 17 Feet Each. Which Expression Shows The Total Area Of These Five Rooms?A. $\left(3 \times 14^{\wedge} 2\right)+\left(2 \times
Understanding the Problem
In this problem, we are given the dimensions of five square rooms, with three rooms measuring 14 feet on each side and two rooms measuring 17 feet on each side. We need to find the total area of these five rooms.
Calculating the Area of a Single Square Room
The area of a square room can be calculated using the formula:
Area = side × side
In this case, the area of each room is:
- For the three rooms with 14-foot sides: 14 × 14 = 196 square feet
- For the two rooms with 17-foot sides: 17 × 17 = 289 square feet
Calculating the Total Area of the Five Rooms
To find the total area of the five rooms, we need to add the areas of all five rooms together. We can do this by adding the areas of the three 14-foot rooms and the two 17-foot rooms.
Let's use the formula for the area of a single room to calculate the total area:
Total Area = (3 × 14^2) + (2 × 17^2)
Evaluating the Expression
Now, let's evaluate the expression to find the total area of the five rooms.
First, we need to calculate the square of each side:
- 14^2 = 196
- 17^2 = 289
Next, we multiply each result by the number of rooms:
- 3 × 196 = 588
- 2 × 289 = 578
Finally, we add the results together to find the total area:
Total Area = 588 + 578 = 1166
Conclusion
In this problem, we were given the dimensions of five square rooms and asked to find the total area of these rooms. We used the formula for the area of a single square room to calculate the area of each room and then added the areas together to find the total area. The correct expression for the total area of the five rooms is:
(3 × 14^2) + (2 × 17^2)
Answer
The correct answer is:
(3 × 14^2) + (2 × 17^2)
Explanation
This expression shows the total area of the five rooms by adding the areas of the three 14-foot rooms and the two 17-foot rooms. The formula for the area of a single room is used to calculate the area of each room, and then the results are added together to find the total area.
Step-by-Step Solution
Here's a step-by-step solution to the problem:
- Calculate the area of each room using the formula: Area = side × side
- Calculate the square of each side: 14^2 = 196, 17^2 = 289
- Multiply each result by the number of rooms: 3 × 196 = 588, 2 × 289 = 578
- Add the results together to find the total area: 588 + 578 = 1166
Final Answer
The final answer is:
Q: What is the formula for the area of a single square room?
A: The formula for the area of a single square room is:
Area = side × side
Q: How do I calculate the area of a room with a side length of 14 feet?
A: To calculate the area of a room with a side length of 14 feet, you can use the formula:
Area = 14 × 14 = 196 square feet
Q: How do I calculate the area of a room with a side length of 17 feet?
A: To calculate the area of a room with a side length of 17 feet, you can use the formula:
Area = 17 × 17 = 289 square feet
Q: What is the total area of the three rooms with 14-foot sides?
A: To find the total area of the three rooms with 14-foot sides, you can multiply the area of a single room by 3:
Total Area = 3 × 196 = 588 square feet
Q: What is the total area of the two rooms with 17-foot sides?
A: To find the total area of the two rooms with 17-foot sides, you can multiply the area of a single room by 2:
Total Area = 2 × 289 = 578 square feet
Q: What is the total area of all five rooms?
A: To find the total area of all five rooms, you can add the total areas of the three 14-foot rooms and the two 17-foot rooms:
Total Area = 588 + 578 = 1166 square feet
Q: What is the correct expression for the total area of the five rooms?
A: The correct expression for the total area of the five rooms is:
(3 × 14^2) + (2 × 17^2)
Q: Why is this expression correct?
A: This expression is correct because it represents the total area of the three 14-foot rooms and the two 17-foot rooms. The formula for the area of a single room is used to calculate the area of each room, and then the results are added together to find the total area.
Q: Can I use a calculator to find the total area of the five rooms?
A: Yes, you can use a calculator to find the total area of the five rooms. Simply enter the expression (3 × 14^2) + (2 × 17^2) into the calculator and press the "calculate" button.
Q: What is the final answer to the problem?
A: The final answer to the problem is:
(3 × 14^2) + (2 × 17^2)
Q: Why is this answer correct?
A: This answer is correct because it represents the total area of the three 14-foot rooms and the two 17-foot rooms. The formula for the area of a single room is used to calculate the area of each room, and then the results are added together to find the total area.
Conclusion
In this article, we have answered some frequently asked questions about the total area of five square rooms. We have provided step-by-step solutions to the problem and explained the correct expression for the total area of the five rooms. We hope that this article has been helpful in understanding the concept of area and how to calculate it.