https://file.aiquickdraw.com/mathbot/file/17270179666077915pdzy.jpg

To find the area of the triangle in the image, we can use **Heron's formula** since the side lengths are given. Heron's formula for the area \( A \) of a triangle is:

\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

where \( a \), \( b \), and \( c \) are the lengths of the sides of the triangle, and \( s \) is the semi-perimeter, given by:

\[
s = \frac{a + b + c}{2}
\]

From the image:
- \( a = 8 \, \text{cm} \)
- \( b = 11 \, \text{cm} \)
- \( c = 13 \, \text{cm} \)

### Step 1: Calculate the semi-perimeter
\[
s = \frac{8 + 11 + 13}{2} = \frac{32}{2} = 16 \, \text{cm}
\]

### Step 2: Apply Heron's formula
\[
A = \sqrt{16(16-8)(16-11)(16-13)}
\]
\[
A = \sqrt{16 \times 8 \times 5 \times 3}
\]
\[
A = \sqrt{16 \times 120} = \sqrt{1920}
\]

Let me calculate that for you.The area of the triangle is approximately \( 43.82 \, \text{cm}^2 \).

Would you like more details on any part of this solution? Here are some related questions:

1. How does Heron's formula work for any triangle?
2. What are other methods to find the area of a triangle?
3. What if one angle of the triangle was given instead of all sides?
4. How would we calculate the perimeter of this triangle?
5. How does the Pythagorean theorem apply to triangles?

**Tip:** Heron's formula is especially useful when you know all three sides of a triangle but not its height!

Work out the area of this triangle with side lengths 8 cm, 11 cm, and 13 cm.

Learn how to find the area of a triangle with sides 8 cm, 11 cm, and 13 cm using Heron's formula. This problem demonstrates geometric principles and the application of Heron's theorem, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation