Priya and Tyler use different methods to find the area of a regular octagon with 7-centimeter sides. Priya decomposes the octagon into 8 identical triangles. Tyler decomposes the octagon into a rectangle and two trapezoids.

2 identical octagons labeled Priya’s method and Tyler’s method.

1. What is the area of the octagon, rounded to the nearest tenth? Type the answer in the box below.

 square centimeters
2.  Explain how to find the area of the octagon using Priya’s method.

### 1. **What is the area of the octagon, rounded to the nearest tenth?**

The area of a regular octagon with side length \( s = 7 \) cm can be calculated using the general formula for the area of a regular octagon:

\[
A = 2(1 + \sqrt{2})s^2
\]

Substitute \( s = 7 \) cm:

\[
A = 2(1 + \sqrt{2})(7)^2 = 2(1 + \sqrt{2})(49)
\]
\[
A = 2(1 + 1.414)(49) = 2(2.414)(49) = 236.572 \, \text{cm}^2
\]

Rounded to the nearest tenth:

\[
A \approx 236.6 \, \text{square centimeters}
\]

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### 2. **Explain how to find the area of the octagon using Priya’s method.**

Priya decomposes the octagon into 8 identical triangles. Here's how to calculate the area using her method:

1. **Step 1: Find the apothem of the octagon.**  
   The ap

Priya and Tyler use different methods to find the area of a regular octagon with 7-centimeter sides. Priya decomposes the octagon into 8 identical triangles. Tyler decomposes the octagon into a rectangle and two trapezoids. 1. What is the area of the octagon, rounded to the nearest tenth? Type the answer in the box below. 2. Explain how to find the area of the octagon using Priya’s method.

Explore how to calculate the area of a regular octagon with 7 cm sides. This problem involves decomposing the octagon using Priya’s triangle method and Tyler’s trapezoid method. Learn key geometry concepts and formulas to solve the problem. Suitable for Grades 9-11.

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