https://file.aiquickdraw.com/mathbot/file/17255581022574d8xe66r.jpg

From the image, the problem is asking to find the value of \( x \) so that the areas of a trapezoid and a rectangle are the same.

### The formula for the area of a trapezoid is given as:
\[
A_{\text{trapezoid}} = \frac{1}{2} h (b_1 + b_2)
\]
where:
- \( h \) is the height (6 ft in the trapezoid),
- \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (one is 12 ft, and the other is \( x \)).

### The formula for the area of a rectangle is:
\[
A_{\text{rectangle}} = \text{length} \times \text{width}
\]
where:
- The length is 12 ft,
- The width is 6 ft.

### Step-by-step solution:

1. **Area of the trapezoid:**
\[
A_{\text{trapezoid}} = \frac{1}{2} \times 6 \times (12 + x) = 3(12 + x) = 36 + 3x
\]

2. **Area of the rectangle:**
\[
A_{\text{rectangle}} = 12 \times 6 = 72
\]

3. **Equating the areas:**
\[
36 + 3x = 72
\]

4. **Solving for \( x \):**
\[
3x = 72 - 36
\]
\[
3x = 36
\]
\[
x = \frac{36}{3} = 12
\]

So, the value of \( x \) is 12 feet.

Would you like more details or have any questions about this? Here are some related questions:

1. How can you check the areas of both shapes after finding \( x \)?
2. What would happen if \( x \) was smaller or larger than 12 ft?
3. Can you apply this method to any trapezoid and rectangle?
4. How do you solve for \( x \) if both shapes have different dimensions?
5. Why does the equation involve adding the base lengths of the trapezoid?

**Tip**: Always ensure to substitute the correct values into area formulas to avoid errors in calculations.

Write and solve an equation to find the value of x so that the figures have the same area. The area of a trapezoid is \( \frac{1}{2} h (b_1 + b_2) \). The two shapes should have the same area.

Learn how to solve for x in a problem where the area of a trapezoid equals the area of a rectangle. This problem covers geometry concepts such as trapezoid area formulas and solving algebraic equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation