https://file.aiquickdraw.com/mathbot/file/17274730439764iggk64v.jpg

To solve the problem of finding the perimeter and area of the polygon with the vertices \( E(6, -2) \), \( F(6, 5) \), and \( G(-1, 5) \), we can follow these steps:

### 1. **Perimeter Calculation**
The perimeter is the sum of the lengths of all the sides of the polygon. Since the polygon is a triangle with vertices \( E(6, -2) \), \( F(6, 5) \), and \( G(-1, 5) \), we need to calculate the distance between each pair of points using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

We'll calculate:
- Distance \( EF \) between \( E(6, -2) \) and \( F(6, 5) \)
- Distance \( FG \) between \( F(6, 5) \) and \( G(-1, 5) \)
- Distance \( GE \) between \( G(-1, 5) \) and \( E(6, -2) \)

### 2. **Area Calculation**
The area of a triangle with vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) can be found using the formula:

\[
\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
\]

Let's first calculate the perimeter and then the area.

I'll do the calculations now.The calculations provide the following results for the polygon with vertices \( E(6, -2) \), \( F(6, 5) \), and \( G(-1, 5) \):

- **Perimeter**: approximately 23.9 units
- **Area**: 24.5 square units

Would you like further details or have any other questions?

Here are 5 related questions you can explore:
1. How would the perimeter and area change if one of the vertices moved?
2. What are other methods to calculate the area of a triangle?
3. Can we generalize the distance formula for higher dimensions?
4. What is the significance of using absolute value in the area formula?
5. How do you find the perimeter and area for polygons with more than three sides?

**Tip:** When calculating distances between points, make sure the coordinates are accurately substituted into the distance formula to avoid errors.

Find the perimeter and area of the polygon with the given vertices E(6, -2), F(6, 5), G(-1, 5).

Learn how to find the perimeter and area of a triangle with vertices E(6, -2), F(6, 5), and G(-1, 5) using the distance and area formulas. This problem covers key geometry concepts, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation