I'm really confused how you do this

Two unequal semicircles, a square , and a rectangle are joined. If the dimensions of the rectangle are 8in by 16in, find the are of the entire region to the nearest 10th.

theres a rectangle in the middle and semi circle on top and side

I sketched it the following way:

a square joined to the width of the rectangle on the left side
A semi-circle on top with diameter along the length of the rectangle.
A semi-circle at the right side of the rectangle with diameter along the width of the rectangle.

Area of square = 64
area of rectangle = 128
area of small sem-circle = (1/2)π(4^2) = 8π
area of large semi-circle = (1/2)π(8^2) = 32π

total = 64+128+8π+32π = .....

the answer is 192 + 40pie

that equals 317.6 inches square

correct

To find the area of the entire region, we need to calculate the areas of the two semicircles and the rectangle separately, and then add them together.

Let's start by finding the area of the rectangle. The formula to calculate the area of a rectangle is length x width. In this case, the length is 16 inches and the width is 8 inches. So, the area of the rectangle is 16 inches x 8 inches = 128 square inches.

Next, let's find the area of the semicircles. The formula to calculate the area of a semicircle is 1/2 x π x radius^2. Since we have two unequal semicircles, we need to calculate their areas separately.

To find the area of the semicircle on top, we need to know its radius. Since it is the same as the width of the rectangle, the radius is 8 inches / 2 = 4 inches. So, the area of the semicircle on top is 1/2 x π x (4 inches)^2 = 1/2 x π x 16 square inches.

To find the area of the semicircle on the side, we need to know its radius as well. As it is the same as the length of the rectangle, the radius is 16 inches / 2 = 8 inches. So, the area of the semicircle on the side is 1/2 x π x (8 inches)^2 = 1/2 x π x 64 square inches.

Now, let's add up the areas of the rectangle and the two semicircles. The total area of the region is 128 square inches + 1/2 x π x 16 square inches + 1/2 x π x 64 square inches.

Using the approximation of π as 3.14, we can calculate the area to the nearest tenth.

Area = 128 + 1/2 x 3.14 x 16 + 1/2 x 3.14 x 64

Finally, calculate the area to get the answer.