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 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 (50 cm²)**: This option represents the product of the base and height without dividing by 2. 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 C (15 cm²)**: This option does not relate to any calculation based on the given base and height. It is incorrect as it does not follow from the area formula. - **Option D (30 cm²)**: Similar to option C, this value does not arise from any correct application of the area formula for the triangle. It is also incorrect. ### Common Pitfalls: - **Forgetting the \(\frac{1}{2}\)**: A frequent mistake is to multiply the base and height directly without dividing by 2, leading to an incorrect area. - **Misunderstanding Base and Height**: Ensure that the base and height are correctly identified. 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 height of 5 cm, the area is 25 cm². - Always remember to divide by 2 when using the area formula for triangles. - Double-check that the base and height are correctly identified and used in calculations.