Read and understand each problem, then solve showing a complete solution 1.) Calculate the area of the shaded region in the right triangle below. 10 cm 5 cm 12 cm 15 cm
The Correct Answer and Explanation is:
The problem asks us to calculate the area of the shaded region in the right triangle. Based on the diagram provided, we can break it down as follows:
Step 1: Understanding the Figure
The right triangle has the following dimensions:
- The base is 10 cm.
- The height is 5 cm.
Step 2: Formula for Area of Triangle
The formula for the area of a right triangle is:Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21×base×height
In this case:
- Base = 10 cm
- Height = 5 cm
Step 3: Calculation
Substitute the known values into the formula:Area=12×10 cm×5 cm=12×50=25 cm2\text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 5 \, \text{cm} = \frac{1}{2} \times 50 = 25 \, \text{cm}^2Area=21×10cm×5cm=21×50=25cm2
Step 4: Conclusion
The area of the entire right triangle is 25 cm².
If the shaded area is just part of this triangle, and the problem asks for that, we’d need to know what fraction or section of the triangle is shaded. However, based on the given data and assuming the entire triangle is shaded, the correct area of the shaded region is 25 cm².
