A triangular hoarding of dimensions 11m, 6m and 15m is used for commerical activities. The hoarding yield an earning of Rs 5000 per `m^(2)` per month. Calculate the total earning by the hoarding in a month [Use `sqrt(2)=1.41`]

Answer

To solve the problem step-by-step, we need to calculate the area of the triangular hoarding using Heron's formula and then find the total earnings based on the area.

### Step 1: Calculate the semi-perimeter (s)
The semi-perimeter \( s \) is calculated using the formula:
\[ s = \frac{a + b + c}{2} \]
where \( a = 11 \, m \), \( b = 6 \, m \), and \( c = 15 \, m \).

Substituting the values:
\[ s = \frac{11 + 6 + 15}{2} = \frac{32}{2} = 16 \, m \]

### Step 2: Apply Heron's formula to find the area (A)
Heron's formula for the area of a triangle is given by:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substituting the values:
\[ A = \sqrt{16(16-11)(16-6)(16-15)} \]
Calculating each term:
\[ A = \sqrt{16 \times 5 \times 10 \times 1} \]
\[ A = \sqrt{16 \times 50} \]
\[ A = \sqrt{800} \]
Breaking it down further:
\[ A = \sqrt{16 \times 50} = 4\sqrt{50} \]
Since \( \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \):
\[ A = 4 \times 5\sqrt{2} = 20\sqrt{2} \, m^2 \]

### Step 3: Calculate the total earnings
The earnings per square meter are given as Rs. 5000. Therefore, the total earnings can be calculated as:
\[ \text{Total Earnings} = \text{Area} \times \text{Earnings per m}^2 \]
Substituting the values:
\[ \text{Total Earnings} = 20\sqrt{2} \times 5000 \]
Using \( \sqrt{2} \approx 1.41 \):
\[ \text{Total Earnings} = 20 \times 1.41 \times 5000 \]
Calculating:
\[ 20 \times 1.41 = 28.2 \]
\[ \text{Total Earnings} = 28.2 \times 5000 = 141000 \]

### Final Answer
The total earning by the hoarding in a month is Rs. 1,41,000.

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