Final answer:
To calculate the area of the compound shape formed by a rectangle and a sector of a circle, find the area of each shape and subtract the overlapping area.
Step-by-step explanation:
To calculate the area of the compound shape formed by a rectangle and a sector of a circle, we need to find the area of each individual shape and then subtract the overlapping area.
1. Find the area of the rectangle by multiplying its length and width.
2. Find the area of the sector of the circle by using the formula (1/2) * radius^2 * angle in radians.
3. Subtract the area of the sector from the area of the rectangle to get the area of the compound shape.
For example, if the rectangle has a length of 10 cm and a width of 5 cm, and the sector has a radius of 4 cm and a central angle of 45 degrees, the area of the compound shape would be calculated as follows:
Area of rectangle = 10 cm * 5 cm = 50 cm^2
Area of sector = (1/2) * 4 cm^2 * (45 degrees/360 degrees) = 1 cm^2 * (0.125) = 0.125 cm^2
Area of compound shape = 50 cm^2 - 0.125 cm^2 = 49.875 cm^2