Two triangular walls of fly over has been used for advertisement . The sides of each wall are 100m ,80m,and 40m .the advertisement yield an earning of rs 1200per meter square per year. Find the amount of revenue earned in one year

To find the revenue earned from the advertisement on the two triangular walls, we first need to calculate the area of each triangular wall. Then, we can multiply the area by the rate of earnings (₹1200 per square meter per year) and double the result since there are two identical triangular walls.

### Step 1: Using Heron's Formula to Calculate the Area of One Triangular Wall

The sides of the triangular wall are 100 m, 80 m, and 40 m. We can use **Heron’s formula** to calculate the area of a triangle when its sides are known.

Heron’s formula is:
\[
\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
\]
Where:
- \( a = 100 \, \text{m} \)
- \( b = 80 \, \text{m} \)
- \( c = 40 \, \text{m} \)
- \( s \) is the semi-perimeter of the triangle, given by:
\[
s = \frac{a + b + c}{2}
\]

Let's calculate the semi-perimeter \( s \):
\[
s = \frac{100 + 80 + 40}{2} = 110 \, \text{m}
\]

Now, we can calculate the area using Heron's formula:
\[
\text{Area} = \sqrt{110(110 - 100)(110 - 80)(110 - 40)}
\]
\[
\text{Area} = \sqrt{110 \times 10 \times 30 \times 70}
\]

### Step 2: Calculate the Revenue

Once the area is calculated, we multiply it by the earnings per square meter (₹1200) and then multiply by 2 because there are two triangular walls.

Let’s perform the calculations.The area of one triangular wall is approximately 1519.87 square meters. The total revenue earned from both triangular walls in one year is approximately ₹3,647,684.20.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this:
1. How is Heron’s formula derived for calculating the area of a triangle?
2. How does the revenue change if the sides of the triangle increase proportionally?
3. What would be the impact on revenue if the rate per square meter increased to ₹1500 per year?
4. How can we calculate the perimeter of the triangle and its relation to the area?
5. Can this method be applied to non-triangular walls, and how would the formula change?

**Tip:** Always verify the accuracy of your measurements and calculations when dealing with irregular shapes for precise results.

Two triangular walls of a flyover have been used for advertisement. The sides of each wall are 100m, 80m, and 40m. The advertisement yields an earning of ₹1200 per square meter per year. Find the amount of revenue earned in one year.

Learn how to calculate the revenue generated from two triangular walls of a flyover, where the sides measure 100m, 80m, and 40m. Using Heron’s formula, calculate the area and multiply it by the advertisement rate of ₹1200 per square meter per year to find the total revenue. Suitable for Grades 9-10.

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