To find the area of a triangle, we can 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 A is Correct: - The calculation shows that the area of the triangle is indeed 25 cm², which corresponds to option A. ### Explanation of Other Options: - **Option B (30 cm²)**: This option is incorrect because it does not match the calculated area. It may arise from a miscalculation or misunderstanding of the area formula. - **Option C (50 cm²)**: This option represents the product of the base and height without taking half, which is a common mistake. The area of a triangle is always half of the rectangle formed by the base and height. - **Option D (15 cm²)**: This option is incorrect and does not relate to any logical calculation based on the given dimensions. It could be a result of random guessing or misapplication of the area formula. ### Common Pitfalls: - **Forgetting to Divide by 2**: A frequent mistake is to forget that the area of a triangle is half the product of the base and height. - **Confusing Base and Height**: Ensure that the base and height are correctly identified; the height must be perpendicular to the base. - **Units**: Always keep track of units. The area will be in square centimeters (cm²) when both base and height are in centimeters. ### 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 base of 10 cm and height of 5 cm, the area is 25 cm². - Always remember to divide by 2 when calculating the area of a triangle. - Ensure that the base and height are correctly identified and measured.