two triangular walls of fly over has been used for advertisement . the sides of each wall are 100m ,80m,and 40m. find the amount of revenue earned in one year .(Take root 231 = 15.2)

To find the revenue earned from the advertisement on the two triangular walls of a flyover, we first need to find the area of one of the triangular walls since the advertisement revenue would likely be based on the area covered.

### Step 1: Finding the Area of the Triangular Wall

The sides of the triangular wall are given as 100 m, 80 m, and 40 m. We can use **Heron's formula** to find the area of a triangle when all three sides are known.

**Heron's formula** states:

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

where:
- \( a = 100 \, \text{m} \)
- \( b = 80 \, \text{m} \)
- \( c = 40 \, \text{m} \)
- \( s = \frac{a + b + c}{2} \) (semi-perimeter)

#### Step 2: Calculating the Semi-Perimeter

\[
s = \frac{100 + 80 + 40}{2} = \frac{220}{2} = 110 \, \text{m}
\]

#### Step 3: Applying Heron's Formula

Now, substituting the values into Heron's formula:

\[
\text{Area} = \sqrt{110 \times (110 - 100) \times (110 - 80) \times (110 - 40)}
\]

Simplify the terms inside the square root:

\[
\text{Area} = \sqrt{110 \times 10 \times 30 \times 70}
\]

Calculating the product:

\[
\text{Area} = \sqrt{110 \times 10 \times 30 \times 70} = \sqrt{2310000}
\]

Given that \(\sqrt{231} = 15.2\), let's find \(\sqrt{2310000}\):

\[
\sqrt{2310000} = 1000 \times \sqrt{231} = 1000 \times 15.2 = 15200 \, \text{m}^2
\]

#### Step 4: Area of Two Walls

Since there are two triangular walls, the total area used for advertisement is:

\[
\text{Total Area} = 2 \times 15200 = 30400 \, \text{m}^2
\]

### Step 5: Finding the Revenue Earned

To find the revenue earned in one year, we would need to know the rate at which revenue is earned per square meter per year. Since this rate isn't provided in the problem, let's denote it as \( R \) (revenue per square meter per year).

The total revenue \( \text{Revenue} \) can be calculated as:

\[
\text{Revenue} = \text{Total Area} \times R = 30400 \times R
\]

### Conclusion

The revenue earned in one year would be \( 30400 \times R \), where \( R \) is the rate of revenue earned per square meter per year.

If you provide the value of \( R \), I can compute the exact revenue amount for you.

---

Would you like further details, or do you have any additional questions?

Here are 5 related questions:
1. What is the formula for calculating the area of a triangle with different types of given measurements?
2. How can we find the height of a triangle if its sides are known?
3. How does Heron's formula work for triangles with larger side lengths?
4. Can you apply Heron's formula to any kind of triangle?
5. What are some common applications of finding the area of a triangle in real life?

**Tip:** When solving geometry problems, identifying all given data and knowing the right formulas is key to solving them correctly.

Two triangular walls of a flyover have been used for advertisement. The sides of each wall are 100m, 80m, and 40m. Find the amount of revenue earned in one year. (Take root 231 = 15.2)

Learn how to calculate the area of two triangular walls with sides 100m, 80m, and 40m using Heron's formula. Understand the application of Heron's theorem and calculate the revenue earned based on the total area. Suitable for Grades 9-10 students.

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