Find the area of the shaded region where a = -2.15 and b = 2.12. Note: the graph may not be drawn to scale.
What graph?
To find the area of the shaded region, we need to determine the area of the two individual shapes that make up the region and then subtract the smaller area from the larger area.
Let's go through the steps to find the areas:
Step 1: Calculate the area of the rectangle.
The rectangle has sides a and b. Since a = -2.15 and b = 2.12, we can calculate the area by multiplying the length and width:
Area of rectangle = a * b = -2.15 * 2.12
Step 2: Calculate the area of the semi-circle.
To calculate the area of a semi-circle, we need to use the formula:
Area of semi-circle = (π * r^2) / 2, where r is the radius of the semi-circle.
In the given graph, we can determine that the radius is equal to |a| since it connects the center of the rectangle to the curved side of the semi-circle. So the radius is | -2.15 | = 2.15.
Plugging in the values, we get:
Area of semi-circle = (π * (2.15)^2) / 2
Step 3: Subtract the area of the smaller shape from the larger shape to get the shaded region.
Area of the shaded region = Area of rectangle - Area of semi-circle
Now, it's time to plug in the given values and calculate the area.