A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
Is there an picture that go to this?
Anonymous you have to have a picture on this.
To find the area of the shaded region, we need to find the areas of both the right triangle and the rectangle, and then subtract the area of the rectangle from the area of the triangle.
Let's start by finding the area of the right triangle. The formula for the area of a triangle is given by half the base multiplied by the height. In this case, the base of the triangle is the length of the bottom side, and the height is the length of the vertical side.
To find the length of the base, we can look at the horizontal side of the triangle, which has a length of 9 units.
To find the length of the height, we can look at the vertical side of the triangle, which has a length of 6 units.
Now we can calculate the area of the right triangle:
Area of the triangle = (1/2) * base * height
= (1/2) * 9 * 6
= 27 units²
Next, we need to find the area of the rectangle. To do this, we need to find the length of the base and the height of the rectangle.
The base of the rectangle is the same as the length of the horizontal side of the triangle, which is 9 units.
To find the height of the rectangle, we can look at the vertical side of the triangle, which is also the height of the rectangle. Therefore, the height of the rectangle is 6 units.
Now we can calculate the area of the rectangle:
Area of the rectangle = base * height
= 9 * 6
= 54 units²
Now that we have the areas of both the triangle and the rectangle, we can find the area of the shaded region by subtracting the area of the rectangle from the area of the triangle:
Area of shaded region = Area of triangle - Area of rectangle
= 27 - 54
= -27 units²
However, we notice that the area of the shaded region is coming out to be negative. This indicates that the rectangle is actually larger than the triangle, and there is no shaded region remaining. Therefore, the area of the shaded region is 0 units².