Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) a = 33, b = 44, c = 21 Need Help? Read It Watch It Master It
Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.) a = 33, b = 44, c = 21 Need Help? Read It Watch It Master It
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
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![**How to Calculate the Area of a Triangle Using Heron's Formula**
Heron's formula is a useful method for finding the area of a triangle when you know the lengths of all three sides. Here’s how you can use it:
Given:
- Side \(a = 33\)
- Side \(b = 44\)
- Side \(c = 21\)
To find the area of the triangle using Heron's formula, follow these steps:
1. **Calculate the Semi-Perimeter:**
\[
s = \frac{a + b + c}{2}
\]
2. **Apply Heron's Formula:**
\[
\text{Area} = \sqrt{s(s - a)(s - b)(s - c)}
\]
3. **Ensure Accuracy:**
- Round your answer to two decimal places for precision.
**Example Calculation:**
1. Compute the semi-perimeter:
\[
s = \frac{33 + 44 + 21}{2} = 49
\]
2. Substitute into Heron's formula:
\[
\text{Area} = \sqrt{49 \times (49 - 33) \times (49 - 44) \times (49 - 21)}
\]
3. Calculate intermediate values and final area:
\[
\text{Area} = \sqrt{49 \times 16 \times 5 \times 28} \approx 297.29
\]
**Need Additional Help?**
- **Read It:** Detailed explanations and step-by-step instructions.
- **Watch It:** Visual and video tutorials to help understand the concept.
- **Master It:** Practice problems with solutions to master Heron's formula.
Ensure to round your final answer to two decimal places for accuracy.
Physics, geometry, and other math-related courses often reference Heron's formula for understanding how to calculate areas when given specific dimensions. Utilize this formula to strengthen your computational skills for various applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61a624e8-9805-4882-bd7c-8b439f9ba0a9%2Fd2371c5b-fc41-4266-9a49-c2d203f5680f%2F9svgy2v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**How to Calculate the Area of a Triangle Using Heron's Formula**
Heron's formula is a useful method for finding the area of a triangle when you know the lengths of all three sides. Here’s how you can use it:
Given:
- Side \(a = 33\)
- Side \(b = 44\)
- Side \(c = 21\)
To find the area of the triangle using Heron's formula, follow these steps:
1. **Calculate the Semi-Perimeter:**
\[
s = \frac{a + b + c}{2}
\]
2. **Apply Heron's Formula:**
\[
\text{Area} = \sqrt{s(s - a)(s - b)(s - c)}
\]
3. **Ensure Accuracy:**
- Round your answer to two decimal places for precision.
**Example Calculation:**
1. Compute the semi-perimeter:
\[
s = \frac{33 + 44 + 21}{2} = 49
\]
2. Substitute into Heron's formula:
\[
\text{Area} = \sqrt{49 \times (49 - 33) \times (49 - 44) \times (49 - 21)}
\]
3. Calculate intermediate values and final area:
\[
\text{Area} = \sqrt{49 \times 16 \times 5 \times 28} \approx 297.29
\]
**Need Additional Help?**
- **Read It:** Detailed explanations and step-by-step instructions.
- **Watch It:** Visual and video tutorials to help understand the concept.
- **Master It:** Practice problems with solutions to master Heron's formula.
Ensure to round your final answer to two decimal places for accuracy.
Physics, geometry, and other math-related courses often reference Heron's formula for understanding how to calculate areas when given specific dimensions. Utilize this formula to strengthen your computational skills for various applications.
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