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 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 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 (40 cm²)**: This option is incorrect because it does not follow from the area formula. If we mistakenly multiplied the base and height without taking half, we would get 60 cm², but halving it correctly gives us 30 cm². - **Option C (60 cm²)**: This option represents the product of the base and height without applying the area formula correctly. The area of a triangle is always half of the rectangle formed by the base and height, so this option is incorrect. - **Option D (20 cm²)**: This option is also incorrect. It could arise from a misunderstanding of the formula or a miscalculation. It does not relate to the correct application of the area formula for a triangle. ### Common Pitfalls - **Forgetting to Divide by 2**: A common mistake is to forget that the area of a triangle is half of the rectangle formed by 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 remember to include the units in your final answer (cm² in this case). ### 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 6 cm, the area is 30 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.