AI
To determine the shaded area, we can use the **Pythagorean theorem** to find the length of the diagonal line, which is the hypotenuse of the right triangle. Then, we can use the **area formula** for a triangle to find the area of the shaded region.
- **Pythagorean theorem**: a^2 + b^2 = c^2, where a and b are the legs of the right triangle and c is the hypotenuse.
- **Area formula**: A = 1/2 bh, where b is the base and h is the height of the triangle.
Using the given side length of the square (20), we can find the length of the diagonal line (c) as follows:
c^2 = 20^2 + 20^2
c^2 = 400 + 400
c^2 = 800
c = √800
c ≈ 28.28
Using the given numbers at the corners of the square (6 and 14), we can find the base (b) and the height (h) of the shaded triangle as follows:
b = 20 - 6 = 14
h = 20 - 14 = 6
Using the area formula, we can find the area of the shaded region (A) as follows:
A = 1/2 bh
A = 1/2 (14)(6)
A = 42
Therefore, the shaded area is approximately **42 square units**.