Final answer:
To find the area of a figure composed of a rectangle and a semicircle, calculate the area of each shape and sum them. The rectangle's area is length times width, and the semicircle's area is half the area of a full circle with the same radius. Combine these values for the total area.
Step-by-step explanation:
To find the area of a figure composed of a rectangle and a semicircle, we need to calculate the area of each shape individually and then sum the areas. The area of a rectangle is found using the formula Area of Rectangle = length × width. To find the area of a semicircle, we first calculate the area of a full circle using the formula Area of Circle = πr² and then divide it by 2, since a semicircle is half of a full circle.
Let's consider the side length of the square enclosing the semicircle to be 'a'. The diameter of the semicircle will be the same as the side of the square, therefore 'a = 2r'. The area of the full circle would thus be πr², and the area of the semicircle will be (πr²)/2. Let's assume that the rectangle's length is 'l' and width is 'w' (which would also be 'a' if it is the same side length as that of the square).
The total area of the figure will be the sum of the rectangle's area and the semicircle's area. So the total area A can be represented as:
Total Area A = lw + (πr²)/2 = lw + (π(a/2)²)/2
Now, plug in the known values for 'l', 'w', and 'a', perform the calculations using the appropriate unit of measure, and round to the nearest tenth. Remember, to maintain accuracy, the number of significant figures in the radius limits the precision of our calculated quantity.