Area Of A Rectangle With Length 7a And Breadth (4a+5b) Is
Introduction
In geometry, the area of a rectangle is a fundamental concept that is used to calculate the space inside the rectangle. The area of a rectangle is calculated by multiplying its length and breadth. In this article, we will discuss the formula for calculating the area of a rectangle with length 7a and breadth (4a+5b).
Understanding the Formula
The formula for calculating the area of a rectangle is given by:
Area = Length x Breadth
In this case, the length of the rectangle is 7a and the breadth is (4a+5b). To calculate the area, we need to multiply the length and breadth.
Calculating the Area
To calculate the area, we need to multiply the length and breadth.
Area = 7a x (4a+5b)
To multiply the length and breadth, we need to follow the order of operations (PEMDAS):
- Multiply 7a and 4a: 7a x 4a = 28a^2
- Multiply 7a and 5b: 7a x 5b = 35ab
- Add the results: 28a^2 + 35ab
Simplifying the Expression
The expression 28a^2 + 35ab can be simplified by factoring out the common term 'a'.
28a^2 + 35ab = a(28a + 35b)
Conclusion
In conclusion, the area of a rectangle with length 7a and breadth (4a+5b) is given by the expression a(28a + 35b). This expression can be used to calculate the area of the rectangle.
Real-World Applications
The concept of area of a rectangle has many real-world applications. For example, in architecture, the area of a room is calculated to determine the amount of furniture that can fit in the room. In engineering, the area of a beam is calculated to determine its strength and stability.
Tips and Tricks
Here are some tips and tricks to help you calculate the area of a rectangle:
- Always follow the order of operations (PEMDAS)
- Factor out common terms to simplify the expression
- Use algebraic manipulations to simplify the expression
Practice Problems
Here are some practice problems to help you practice calculating the area of a rectangle:
- Find the area of a rectangle with length 3x and breadth (2x+4y)
- Find the area of a rectangle with length 5y and breadth (3y+2z)
- Find the area of a rectangle with length 2z and breadth (4z+3w)
Conclusion
In conclusion, the area of a rectangle with length 7a and breadth (4a+5b) is given by the expression a(28a + 35b). This expression can be used to calculate the area of the rectangle. We hope this article has helped you understand the formula and calculations for calculating the area of a rectangle.
Introduction
In our previous article, we discussed the formula and calculations for calculating the area of a rectangle with length 7a and breadth (4a+5b). In this article, we will answer some frequently asked questions related to the area of a rectangle.
Q: What is the formula for calculating the area of a rectangle?
A: The formula for calculating the area of a rectangle is given by:
Area = Length x Breadth
Q: How do I calculate the area of a rectangle with length 3x and breadth (2x+4y)?
A: To calculate the area, you need to multiply the length and breadth.
Area = 3x x (2x+4y) = 3x(2x+4y) = 6x^2 + 12xy
Q: What is the difference between the area of a rectangle and the perimeter of a rectangle?
A: The area of a rectangle is the space inside the rectangle, while the perimeter of a rectangle is the distance around the rectangle. The formula for calculating the perimeter of a rectangle is given by:
Perimeter = 2(Length + Breadth)
Q: How do I calculate the area of a rectangle with length 5y and breadth (3y+2z)?
A: To calculate the area, you need to multiply the length and breadth.
Area = 5y x (3y+2z) = 5y(3y+2z) = 15y^2 + 10yz
Q: What is the significance of the order of operations (PEMDAS) in calculating the area of a rectangle?
A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. In the case of calculating the area of a rectangle, we need to follow the order of operations to ensure that we get the correct result.
Q: How do I simplify an expression like 28a^2 + 35ab?
A: To simplify the expression, you can factor out the common term 'a'.
28a^2 + 35ab = a(28a + 35b)
Q: What are some real-world applications of the area of a rectangle?
A: The area of a rectangle has many real-world applications, such as:
- Calculating the area of a room to determine the amount of furniture that can fit in the room
- Calculating the area of a beam to determine its strength and stability
- Calculating the area of a plot of land to determine its value
Q: How do I practice calculating the area of a rectangle?
A: You can practice calculating the area of a rectangle by:
- Using online calculators or worksheets to practice different types of problems
- Creating your own problems and solving them
- Working with a partner or tutor to practice and get feedback
Conclusion
In conclusion, we hope this article has helped you understand some frequently asked questions related to the area of a rectangle. Remember to always follow the order of operations (PEMDAS) and to simplify expressions by factoring out common terms. With practice and patience, you will become proficient in calculating the area of a rectangle.