https://file.aiquickdraw.com/mathbot/file/1723168296765wzwfe6i8.jpg

**The area of the triangle pictured below is 880 square inches.**


The image shows a right triangle with legs of lengths 40 inches and 44 inches. You’ve mentioned that the area of this triangle is \(880\) square inches. Let's verify this and discuss any additional calculations needed.

### Step 1: Calculate the Area of the Triangle
The area \(A\) of a right triangle is calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

Here, the base is \(44\) inches, and the height is \(40\) inches.

\[
A = \frac{1}{2} \times 44 \times 40 = \frac{1}{2} \times 1760 = 880 \text{ square inches}
\]

This confirms that the area of the triangle is indeed \(880\) square inches.

### Step 2: Calculate the Hypotenuse (Optional)
To find the length of the hypotenuse, \(c\), we can use the Pythagorean theorem:

\[
c = \sqrt{\text{base}^2 + \text{height}^2}
\]

\[
c = \sqrt{44^2 + 40^2} = \sqrt{1936 + 1600} = \sqrt{3536}
\]

\[
c \approx 59.49 \text{ inches}
\]

### Summary
- **Area** of the triangle = \(880\) square inches (confirmed).
- **Hypotenuse** length \(c\) ≈ \(59.49\) inches.

Do you have any questions or would you like more details on any step?

Here are 8 related questions:
1. How is the area of a right triangle related to its base and height?
2. What is the Pythagorean theorem, and how is it used?
3. Can you calculate the area of a triangle with different base and height lengths?
4. What is the perimeter of this right triangle, including the hypotenuse?
5. How do you find the missing side of a right triangle if you know the hypotenuse and one leg?
6. How does the area of this right triangle compare to that of a square with the same base and height?
7. If the height were doubled, how would the area of the triangle change?
8. What are some real-world applications of calculating the area of a triangle?

**Tip:** In a right triangle, always verify whether you’re dealing with the correct base and height (the legs) when calculating the area.

Learn how to calculate the area of a right triangle with legs measuring 40 and 44 inches. Includes step-by-step calculations using the area formula for triangles and verification of the result. Suitable for students in Grades 7-9.

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