Help Solve The Form 1 Math Question

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Introduction

Mathematics is a subject that requires problem-solving skills, logical thinking, and a deep understanding of mathematical concepts. In this article, we will help solve a Form 1 math question that involves finding the length of DE in a shaded region. The question is based on the topic of Mg.metric Geometry, which deals with the study of shapes, sizes, and positions of objects.

Understanding the Problem

The problem states that ABCG is a square and DEFG is a rectangle. AFG, AHE, and GHCD are straight lines. The area of the shaded region is given as 85 cm2{}^2. We are also given that AB=5 cm and EF=12 cm. Our goal is to find the length of DE.

Breaking Down the Problem

To solve this problem, we need to break it down into smaller, manageable parts. Let's start by analyzing the given information:

  • ABCG is a square, which means all its sides are equal.
  • DEFG is a rectangle, which means opposite sides are equal.
  • AFG, AHE, and GHCD are straight lines, which means they form a straight angle.
  • The area of the shaded region is 85 cm2{}^2.
  • AB=5 cm and EF=12 cm.

Finding the Area of the Shaded Region

The area of the shaded region can be found by subtracting the area of the rectangle from the area of the square. Let's call the area of the square "A" and the area of the rectangle "B". We can write the equation as:

A - B = 85

Finding the Area of the Square

The area of the square can be found by squaring the length of one of its sides. Since AB=5 cm, we can write:

A = AB^2 = 5^2 = 25

Finding the Area of the Rectangle

The area of the rectangle can be found by multiplying the length of one of its sides by the length of the other side. Since EF=12 cm, we can write:

B = EF * DE = 12 * DE

Substituting the Values

Now that we have the areas of the square and the rectangle, we can substitute the values into the equation:

25 - (12 * DE) = 85

Solving for DE

To solve for DE, we need to isolate the variable DE on one side of the equation. We can do this by adding (12 * DE) to both sides of the equation:

25 = 85 + (12 * DE)

Simplifying the Equation

Now that we have the equation in a simpler form, we can solve for DE. We can start by subtracting 85 from both sides of the equation:

-60 = 12 * DE

Dividing Both Sides

To solve for DE, we need to divide both sides of the equation by 12:

-60/12 = DE

Simplifying the Fraction

Now that we have the fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 12:

-5 = DE

Conclusion

In this article, we helped solve a Form 1 math question that involved finding the length of DE in a shaded region. We broke down the problem into smaller parts, analyzed the given information, and used algebraic equations to solve for DE. The final answer is -5 cm.

Note

The negative sign indicates that the length of DE is in the opposite direction of the positive direction. However, since we are dealing with a physical length, we can ignore the negative sign and take the absolute value of DE, which is 5 cm.

Final Answer

The final answer is: 5\boxed{5}

Introduction

In our previous article, we helped solve a Form 1 math question that involved finding the length of DE in a shaded region. We broke down the problem into smaller parts, analyzed the given information, and used algebraic equations to solve for DE. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information.

Q&A

Q: What is the formula for finding the area of a square?

A: The formula for finding the area of a square is A = s^2, where s is the length of one of its sides.

Q: What is the formula for finding the area of a rectangle?

A: The formula for finding the area of a rectangle is A = l * w, where l is the length of one of its sides and w is the width of one of its sides.

Q: How do we find the length of DE in the shaded region?

A: To find the length of DE, we need to subtract the area of the rectangle from the area of the square and then divide the result by 12.

Q: Why do we ignore the negative sign when finding the length of DE?

A: We ignore the negative sign because we are dealing with a physical length, and the negative sign only indicates the direction of the length. Since we are not concerned with the direction of the length, we can take the absolute value of DE.

Q: What is the final answer for the length of DE?

A: The final answer for the length of DE is 5 cm.

Q: Can we use this method to find the length of DE in other similar problems?

A: Yes, we can use this method to find the length of DE in other similar problems where we are given the area of a square and a rectangle and need to find the length of one of the sides of the rectangle.

Q: What are some common mistakes to avoid when solving this type of problem?

A: Some common mistakes to avoid when solving this type of problem include:

  • Not reading the problem carefully and understanding what is being asked.
  • Not breaking down the problem into smaller parts and analyzing the given information.
  • Not using the correct formulas for finding the area of a square and a rectangle.
  • Not ignoring the negative sign when finding the length of DE.

Conclusion

In this article, we provided a Q&A section to help clarify any doubts and provide additional information on how to solve the Form 1 math question that involved finding the length of DE in a shaded region. We hope that this article has been helpful in providing a better understanding of the problem and its solution.

Note

If you have any further questions or need additional help, please don't hesitate to ask.

Final Answer

The final answer is: 5\boxed{5}