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 Result**: - Therefore, the area of the triangle is \(25 \, \text{cm}^2\). ### Conclusion The correct option is **A. 25 cm²**. ### Explanation of Other Options - **Option B (30 cm²)**: This option is incorrect because it does not follow the area formula. If we mistakenly added the base and height instead of multiplying, we might think the area is larger, but that is not how area is calculated. - **Option C (50 cm²)**: This option represents the product of the base and height without taking half. While it is a common mistake to forget the \(\frac{1}{2}\) in the area formula, it does not represent the area of a triangle. - **Option D (15 cm²)**: This option is incorrect and does not relate to any logical calculation based on the given dimensions. It could arise from a misunderstanding of the formula or incorrect arithmetic. ### Common Pitfalls - **Forgetting the \(\frac{1}{2}\)**: A frequent mistake is to multiply the base and height directly without dividing by 2. - **Confusing Area with Perimeter**: Remember that area measures the space within the triangle, while perimeter measures the distance around it. - **Units**: Always ensure that the units are consistent (in this case, cm) and remember to square the units when calculating area (cm²). ### 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 height of 5 cm, the area is \(25 \, \text{cm}^2\). - Always remember to include the \(\frac{1}{2}\) in the area formula. - Be cautious of common mistakes such as miscalculating or confusing area with perimeter.