Look at the trapezoid in the figure.
Express the perimeter of the trapezoid using the given variables.
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Look at the trapezoid in the figure.
Express the perimeter of the trapezoid using the given variables.
To solve this problem, we'll express the perimeter of the trapezoid by summing up its side lengths:
Step 1: Identify the given side lengths.
Step 2: Apply the perimeter formula for the trapezoid.
Step 3: Simplify the resulting expression.
Let's work through these steps:
Step 1: The trapezoid has the following side lengths:
- Top base:
- Left side:
- Bottom base:
- Right side:
Step 2: Apply the perimeter formula:
The perimeter is given by the sum of all sides:
\begin{equation}
Step 3: Simplify the expression:
Combine like terms:
Therefore, the perimeter of the trapezoid is expressed as .
8X+3Y+Z
Given the trapezoid:
What is the area?
Like terms have the same variable and exponent! Since 5X and 3X both have just 'X', you can add them: 5X + 3X = 8X. But Z and 3Y have different variables, so they stay separate.
That's mathematically correct! Addition is commutative, meaning order doesn't change the result. However, it's conventional to write terms in alphabetical order or with like terms grouped together.
A trapezoid has exactly one pair of parallel sides. In the diagram, you can see the top and bottom sides are horizontal (parallel), while the left and right sides are slanted and not parallel to each other.
No, this expression is fully simplified! Since 8X, 3Y, and Z all have different variables or coefficients, there are no more like terms to combine.
Perimeter is the total distance around the outside of a shape. Think of it like walking around the edge - you'd travel along each side exactly once, so you add all the side lengths together.
The problem asks for an algebraic expression using the given variables. This means we express the perimeter in terms of X, Y, and Z rather than finding a specific number value.
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