To find the area of a triangle, we use the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] ### Step-by-Step Explanation 1. **Identify the Base and Height**: - In this problem, the base of the triangle is given as 10 cm, and the height is given as 5 cm. 2. **Substitute the Values into the Formula**: - We substitute the values of the base and height into the area formula: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 5 \, \text{cm} \] 3. **Perform the Multiplication**: - First, multiply the base and height: \[ 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2 \] 4. **Multiply by \(\frac{1}{2}\)**: - Now, take half of the result: \[ \text{Area} = \frac{1}{2} \times 50 \, \text{cm}^2 = 25 \, \text{cm}^2 \] 5. **Final Answer**: - Therefore, the area of the triangle is **25 cm²**. ### Why Option B is Correct - The calculation shows that the area of the triangle is indeed 25 cm², which corresponds to option B. ### Explanation of Other Options - **Option A: 15 cm²**: This option is incorrect because it underestimates the area. The calculation clearly shows that the area is larger than 15 cm². - **Option C: 50 cm²**: This option is incorrect because it represents the area of a rectangle with the same base and height, not a triangle. The area of a triangle is always half of that of a rectangle with the same base and height. - **Option D: 30 cm²**: This option is also incorrect. It does not correspond to any logical calculation based on the given dimensions of the triangle. ### Common Pitfalls - **Forgetting to Divide by 2**: A common mistake is to forget that the area of a triangle is half of the area of a rectangle. Always remember to include the \(\frac{1}{2}\) in the formula. - **Misidentifying Base and Height**: Ensure that you correctly identify which dimension is the base and which is the height. The height must be perpendicular to the base. ### Revision Summary - The area of a triangle is calculated using the formula: \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\). - For a triangle with a base of 10 cm and a height of 5 cm, the area is 25 cm². - Always remember to divide by 2 when calculating the area of a triangle. - Be careful to correctly identify the base and height to avoid calculation errors.