https://file.aiquickdraw.com/mathbot/file/172401479392759j275c6.jpg

Find the perimeter and area for this triangle

Let's analyze the triangle in the image to find its perimeter and area. The triangle has the following side lengths:

- One side: \(9 \, \text{m}\)
- Another side: \(14 \, \text{m}\)
- The third side is split into two parts, \(7 \, \text{m}\) and \(4 \, \text{m}\), with the sum giving \(7 + 4 = 11 \, \text{m}\).

### Perimeter
The perimeter \( P \) of the triangle is the sum of all three sides:
\[
P = 9 \, \text{m} + 14 \, \text{m} + 11 \, \text{m} = 34 \, \text{m}
\]

### Area
To find the area of the triangle, we can use the formula:
\[
A = \frac{1}{2} \times \text{Base} \times \text{Height}
\]
Here, the base is \(9 \, \text{m}\) (as shown on the diagram), and the height corresponding to this base is \(4 \, \text{m}\).

\[
A = \frac{1}{2} \times 9 \, \text{m} \times 4 \, \text{m} = \frac{1}{2} \times 36 \, \text{m}^2 = 18 \, \text{m}^2
\]

### Summary:
- **Perimeter:** 34 meters
- **Area:** 18 square meters

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What would the area be if the height of the triangle increased to 6 meters?
2. How would the perimeter change if the side of 14 meters was shortened by 3 meters?
3. If the base was extended to 12 meters, how would the area of the triangle change?
4. Can you calculate the area if a new height of 5 meters is given for the same base?
5. How does the area change if the entire triangle is scaled up by a factor of 2?

**Tip:** When dealing with triangles, always ensure you identify the correct base and corresponding height, as these directly impact the area calculation.

Learn how to calculate the perimeter and area of a triangle with sides 9m, 14m, and 11m using the formulas for triangle perimeter and area. This problem involves basic triangle properties and is suitable for students in Grades 6-8.

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