https://file.aiquickdraw.com/mathbot/file/1728369395623hjub8x2i.jpg

In the image, we see a right-angled triangle. The base of the triangle is given as 3 units, and the height is 5 units. The hypotenuse is labeled as \(4\sqrt{10}\). The task is to find the area of the shaded region, which is the area of the triangle.

The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Here, the base is 3 units, and the height is 5 units. Substituting these values into the formula:

\[
\text{Area} = \frac{1}{2} \times 3 \times 5 = \frac{15}{2} = 7.5 \, \text{square units}
\]

Thus, the area of the shaded region is **7.5 square units**.

Would you like further details or have any questions?

Here are five related questions to further your understanding:
1. How do you find the hypotenuse of a right triangle using the Pythagorean theorem?
2. What is the formula for finding the perimeter of a triangle?
3. How does the area of a triangle change if both the base and height are doubled?
4. Can you calculate the hypotenuse directly from the given base and height using any formula?
5. How would you calculate the area if the triangle was not a right triangle?

**Tip:** Always ensure you use the right values for the base and height, especially when dealing with right triangles—make sure the right-angle corner defines these sides.

The area of the shaded region in a right-angled triangle with base 3 units, height 5 units, and hypotenuse 4√10 is required.

Calculate the area of the shaded region in a right-angled triangle with a base of 3 units, a height of 5 units, and a hypotenuse of 4√10. Learn the step-by-step solution using the area of a triangle formula, suitable for Grades 6-8.

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