Finding Equilateral Triangle Area
The problem asks for the area of an equilateral triangle with a side length of 10 m.
Equilateral Triangle Area Formula
The area ($A$) of an equilateral triangle with side length ($s$) is given by the formula:
$ A = \frac{\sqrt{3}}{4} s^2 $
Calculating the Area
Given the side length $s = 10$ m, substitute this value into the formula:
- $ A = \frac{\sqrt{3}}{4} (10 \text{ m})^2 $
- $ A = \frac{\sqrt{3}}{4} \times 100 \text{ m}^2 $
- $ A = 25\sqrt{3} \text{ m}^2 $
Approximating the Value
Using the approximate value of $ \sqrt{3} \approx 1.732 $:
- $ A \approx 25 \times 1.732 \text{ m}^2 $
- $ A \approx 43.30 \text{ m}^2 $
Comparing with Options
Now, compare the calculated area ($ \approx 43.30 \text{ m}^2 $) with the given options:
- Option 1: $42.25\text{ m}^2$
- Option 2: $45.25\text{ m}^2$
- Option 3: $43.25\text{ m}^2$
- Option 4: $44.25\text{ m}^2$
The calculated area, $43.30 \text{ m}^2$, is closest to Option 3, $43.25 \text{ m}^2$.
Similar Questions
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Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
