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**: - Plugging the values into the area formula, we have: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} \] 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, 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 product of the base and height without dividing by 2. While it is the correct product of base and height, it does not account for the fact that we need to take half of that product to find the area of a triangle. - **Option C (15 cm²)**: This option is incorrect as it does not reflect any correct calculation based on the given base and height. It could arise from a misunderstanding of the formula or incorrect arithmetic. - **Option D (20 cm²)**: This option is also incorrect. It may result from an error in calculation, such as mistakenly using a different base or height or misapplying the area formula. ### Common Pitfalls: - **Forgetting to Divide by 2**: A common mistake is to forget that the area of a triangle is half the product of the base and height. - **Misidentifying 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 6 cm, the area is 30 cm². - Remember to divide the product of base and height by 2 to find the area. - Always check your calculations and ensure you are using the correct units.