To solve the problem of finding the unknown lengths in the given compound shapes, we need to carefully analyze each shape and use the information provided (such as the total perimeter or other known dimensions) to determine the missing lengths. Below is a step-by-step explanation for solving these types of problems.
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General Approach:
1.
Understand the Shape: Identify the structure of the compound shape and how its sides are arranged.
2.
Use Perimeter Information: If the perimeter is given, use the formula for the perimeter of a rectangle or other relevant geometric principles.
3.
Label Known and Unknown Sides: Assign variables to the unknown lengths and use the relationships between the sides to form equations.
4.
Solve for Unknowns: Use algebraic methods to solve for the unknown lengths.
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Example Problem Solving:
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Problem 1:
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Shape: A compound shape with some labeled sides.
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Given: Perimeter = 30 units.
-
Unknown: Length of one side.
Steps:
1.
Identify the Sides: Label all the sides, including the unknown ones.
2.
Sum the Perimeter: Add up all the sides, including the unknowns.
3.
Set Up an Equation: Use the given perimeter to form an equation.
4.
Solve for the Unknown: Solve the equation to find the missing length.
Example Calculation:
Suppose the shape has sides labeled as follows:
- Top side: 5 units
- Bottom side: 5 units
- Left side: 4 units
- Right side: Unknown (let’s call it \( x \))
- Other internal sides: 3 units each
The perimeter is the sum of all the outer sides:
\[
5 + 5 + 4 + x + 3 + 3 = 30
\]
Simplify:
\[
20 + x = 30
\]
Solve for \( x \):
\[
x = 10
\]
So, the unknown length is \( \boxed{10} \).
---
####
Problem 2:
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Shape: Another compound shape with different dimensions.
-
Given: Perimeter = 40 units.
-
Unknown: Length of one side.
Steps:
1.
Identify the Sides: Label all the sides, including the unknown ones.
2.
Sum the Perimeter: Add up all the sides, including the unknowns.
3.
Set Up an Equation: Use the given perimeter to form an equation.
4.
Solve for the Unknown: Solve the equation to find the missing length.
Example Calculation:
Suppose the shape has sides labeled as follows:
- Top side: 6 units
- Bottom side: 6 units
- Left side: 5 units
- Right side: Unknown (let’s call it \( y \))
- Other internal sides: 4 units each
The perimeter is the sum of all the outer sides:
\[
6 + 6 + 5 + y + 4 + 4 = 40
\]
Simplify:
\[
25 + y = 40
\]
Solve for \( y \):
\[
y = 15
\]
So, the unknown length is \( \boxed{15} \).
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Key Points to Remember:
- Always label all known and unknown sides.
- Use the perimeter formula or other geometric relationships to set up equations.
- Solve the equations systematically.
If you provide specific details from the image, I can solve those problems directly. Otherwise, the above approach should help you tackle similar problems.
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Final Answer:
\[
\boxed{\text{Follow the steps outlined above to solve for the unknown lengths in each compound shape.}}
\]
Parent Tip: Review the logic above to help your child master the concept of perimeter worksheet with missing sides.
