I am supposed to find the area of a segment of a circle. The circle is cut with two radi with an angle of 90 degrees. Then where the radi touch the circle another line is drawn to connect them. The triangle and the small section between the triangle and the edge of the circle are the shaded areas. It also tells me that the unshaded area of the circle is 3 m.
Wow! Ed, Hannah, Becca, Rebecca, Shelby, Sarah, Izzy, and Becky!
8 different names this evening! I think you've set a record!
Please use the same name for your posts.
I am not all those people
They all came from the same computer.
To find the area of the shaded segment, we need to follow a few steps:
Step 1: Find the area of the entire circle
The unshaded area of the circle is given as 3 m. Since the shaded segment is a part of the circle, we need to find the area of the entire circle first.
Step 2: Find the area of the triangle
The two radii form a right triangle with the segment of the circle. To find the area of the triangle, we can use the formula:
Area of a triangle = 1/2 * base * height
In this case, the base of the triangle is the length of one of the radii, and the height is the distance between the center of the circle and the point where the radii touch the circle. Since the radii touch the circle at right angles, the height is equal to the radius.
Step 3: Find the area of the sector
The sector is the shaded section between the triangle and the edge of the circle. To find its area, we need to calculate the angle of the sector.
Since the radii form a right angle, one of the radii divides the circle into two sectors with equal angles. The given angle between the radii is 90 degrees, which means each sector has an angle of 45 degrees.
To find the area of the sector, we can use the formula:
Area of a sector = (angle/360) * π * r^2
where angle is the measure of the central angle in degrees, π is a mathematical constant (approximately 3.14), and r is the radius of the circle.
Step 4: Calculate the shaded segment area
To find the area of the shaded segment, subtract the area of the triangle and the sector from the total area of the circle.
Shaded segment area = Total area of the circle - Area of the triangle - Area of the sector
That's how you can find the area of the shaded segment of a circle given the described scenario.