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 6 cm. 2. **Substitute the Values into the Formula**: - We substitute the values of the base and height into the area formula: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} \] 3. **Calculate the Product of Base and Height**: - First, calculate the product of the base and height: \[ 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2 \] 4. **Multiply by \(\frac{1}{2}\)**: - Now, we take half of this product: \[ \text{Area} = \frac{1}{2} \times 60 \, \text{cm}^2 = 30 \, \text{cm}^2 \] 5. **Final Answer**: - Therefore, the area of the triangle is **30 cm²**. ### Why Option A is Correct - The calculation shows that the area of the triangle is indeed 30 cm², which corresponds to option A. ### Explanation of Other Options - **Option B (60 cm²)**: This option represents the total area calculated from the base and height without applying the \(\frac{1}{2}\) factor. It is incorrect because the area of a triangle is always half of the rectangle formed by the base and height. - **Option C (20 cm²)**: This option is incorrect as it does not reflect any correct calculation based on the given dimensions. It may arise from a misunderstanding of the area formula or incorrect arithmetic. - **Option D (50 cm²)**: This option is also incorrect. It does not correspond to any logical calculation based on the provided dimensions. It may stem from an incorrect application of the area formula or miscalculation. ### Common Pitfalls - **Forgetting the \(\frac{1}{2}\)**: A common mistake is to forget to multiply by \(\frac{1}{2}\) when calculating the area of a triangle, leading to the incorrect assumption that the area is equal to the product of the base and height. - **Misreading Dimensions**: Ensure that the base and height are correctly identified. Sometimes, students may confuse the dimensions or misinterpret the problem. ### 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 6 cm, the area is 30 cm². - Always remember to include the \(\frac{1}{2}\) factor in the area formula for triangles. - Double-check your calculations to avoid common mistakes.