The area of the largest triangle that can be inscribed in a semicircle of radius 6 m is

Options

A. `36 m^(2)`
B. `72 m^(2)`
C. `18 m^(2)`
D. `12 m^(2)`

Answer

To find the area of the largest triangle that can be inscribed in a semicircle of radius 6 m, we can follow these steps:

### Step 1: Understand the Geometry
The largest triangle that can be inscribed in a semicircle is a right triangle, where the hypotenuse is the diameter of the semicircle. The radius of the semicircle is given as 6 m.

### Step 2: Identify the Base and Height
In this case, the base of the triangle will be the diameter of the semicircle. Since the radius is 6 m, the diameter (base) will be:
\[ \text{Diameter} = 2 \times \text{Radius} = 2 \times 6 = 12 \text{ m} \]

The height of the triangle will be equal to the radius of the semicircle, which is 6 m.

### Step 3: Calculate the Area of the Triangle
The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Substituting the values we found:
\[ A = \frac{1}{2} \times 12 \text{ m} \times 6 \text{ m} \]

### Step 4: Perform the Calculation
Now, calculate the area:
\[ A = \frac{1}{2} \times 12 \times 6 = \frac{72}{2} = 36 \text{ m}^2 \]

### Conclusion
The area of the largest triangle that can be inscribed in a semicircle of radius 6 m is:
\[ \boxed{36 \text{ m}^2} \]

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