how many trees are planted in a trapezoidal garden with sides of 24 m, 16 m, arms of 34 m and 26 m and a height of 15 m if one tree needs 6m^2?

To determine how many trees can be planted in a trapezoidal garden, we need to calculate the area of the trapezoid and then divide it by the area needed for each tree.

### Step 1: Calculate the Area of the Trapezoidal Garden
For a trapezoid, the area \( A \) can be calculated using the formula:
\[
A = \frac{1}{2} \times (a + b) \times h
\]
where:
- \( a = 24 \, \text{m} \) (one parallel side),
- \( b = 16 \, \text{m} \) (the other parallel side),
- \( h = 15 \, \text{m} \) (the height).

Substituting the values:
\[
A = \frac{1}{2} \times (24 + 16) \times 15
\]
\[
A = \frac{1}{2} \times 40 \times 15
\]
\[
A = 20 \times 15 = 300 \, \text{m}^2
\]

### Step 2: Calculate the Number of Trees
Each tree requires \( 6 \, \text{m}^2 \). To find the number of trees \( N \), divide the area of the garden by the area required per tree:
\[
N = \frac{300}{6} = 50
\]

### Conclusion
The number of trees that can be planted in the garden is:
\[
\boxed{50}
\]

Would you like further details on trapezoidal area calculation, or do you have any questions?

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Here are 5 related questions for further exploration:
1. What if the area requirement per tree changes to 8 m²? How would that affect the number of trees?
2. How would the calculation change if the height of the trapezoid was increased to 20 m?
3. How do you calculate the perimeter of a trapezoid, and why might this be useful?
4. Can a trapezoid's area be found using a different approach, such as coordinate geometry?
5. How is the planting pattern affected by the shape of the garden?

**Tip:** Remember, when dealing with irregular plots, the formula for area remains consistent, but visualizing the shape with a sketch can help avoid mistakes.

Find out how to calculate the number of trees that can be planted in a trapezoidal garden with sides of 24 m and 16 m, arms of 34 m and 26 m, and a height of 15 m. This geometry problem includes step-by-step calculations using the trapezoid area formula, suitable for Grades 6-8.

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