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 B is Correct - The correct answer is **B. 25 cm²** because we followed the correct formula for the area of a triangle and substituted the values accurately. The calculations confirm that the area is indeed 25 cm². ### Why the Other Options are Incorrect - **Option A: 15 cm²** - This option is incorrect because it does not result from the correct application of the area formula. It may arise from a miscalculation or misunderstanding of the formula. - **Option C: 30 cm²** - This option is also incorrect. It could result from incorrectly multiplying the base and height or misunderstanding the concept of halving the product. - **Option D: 50 cm²** - This option represents the product of the base and height without applying the \(\frac{1}{2}\) factor. It is a common mistake to forget to divide by 2 when calculating the area of a triangle. ### Common Pitfalls - **Forgetting the \(\frac{1}{2}\)**: A frequent mistake is to multiply the base and height without dividing by 2, leading to an area that is twice the actual value. - **Confusing Base and Height**: Ensure that the base and height are correctly identified. The height must be perpendicular to the base. - **Units**: Always include the units in your final answer. In this case, the area is in square centimeters (cm²). ### 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. - Remember to always divide the product of base and height by 2. - Be cautious with units and ensure the height is perpendicular to the base.