Respuesta :
Step-by-step explanation:
To find the area of the figure described, we need to calculate the area of the rectangle and the area of the two semicircles on each end, then add them together.Step 1: Calculate the area of the rectangle.The length of the rectangle is the length of the major axis of the ellipse, which is 8 inches. However, since there are semicircles on each end, we need to subtract the diameters of the semicircles from the total length to get the length of the rectangle part.The diameter of each semicircle is the length of the minor axis of the ellipse, which is 6 inches. Since there are two semicircles, the total length subtracted from the major axis will be 6 inches (the diameter of one semicircle, not both, because the semicircles are on the ends of the major axis).So, the length of the rectangle is 8 inches - 6 inches = 2 inches.The width of the rectangle is the same as the diameter of the semicircles, which is 6 inches.Now, we can calculate the area of the rectangle:Area of rectangle = length × widthArea of rectangle = 2 inches × 6 inchesArea of rectangle = 12 square inchesStep 2: Calculate the area of the two semicircles.First, we find the area of a full circle with the diameter of 6 inches and then divide it by 2 to get the area of a semicircle. Since there are two semicircles, we will multiply the area of one semicircle by 2.The radius of the semicircle is half of the diameter, so the radius r is 6 inches / 2 = 3 inches.Area of a full circle = π × r^2Using 3.14 for π, we get:Area of a full circle = 3.14 × (3 inches)^2Area of a full circle = 3.14 × 9 square inchesArea of a full circle = 28.26 square inchesNow, the area of one semicircle is half of this:Area of one semicircle = 28.26 square inches / 2Area of one semicircle = 14.13 square inchesSince there are two semicircles, we multiply this by 2:Area of two semicircles = 14.13 square inches × 2Area of two semicircles = 28.26 square inchesStep 3: Add the area of the rectangle and the area of the two semicircles to get the total area of the figure.Total area = Area of rectangle + Area of two semicirclesTotal area = 12 square inches + 28.26 square inchesTotal area = 40.26 square inchesRounding to the nearest tenth, the total area is 40.3 square inches.However, none of the answer choices match this calculation. It seems there might be a misunderstanding in the interpretation of the picture details or the question. If the figure is indeed a rectangle with a semicircle on each end, and the dimensions provided are correct, then the answer should be 40.3 square inches, which is not listed in the options provided. Please double-check the details of the question and the picture to ensure the correct dimensions and figure are being described.
