Answer:
A = 100π + 144 square yards.
Explanation:
To write the equation for the area of a compound shape consisting of a circle with a square inscribed in it, we can first find the individual areas of the circle and the square, and then add them together.The diameter of the circle would be equal to the diagonal of the inscribed square. The diagonal of a square with side length s can be found using the Pythagorean theorem as √(s^2 + s^2) = s√2. Therefore, the diameter of the circle would be 20 yards, since the side length of the square is 12 yards.The area of the circle can be calculated using the formula A = πr^2, where r is the radius of the circle. Since the diameter of the circle is 20 yards, the radius would be half of that, or 10 yards. So, the area of the circle would be:A_circle = π(10)^2 = 100π square yards.The area of the square can be calculated using the formula A = s^2, where s is the length of a side of the square. Since the side length of the square is 12 yards, the area of the square would be:A_square = (12)^2 = 144 square yards.To find the total area of the compound shape, we can add the areas of the circle and the square:A_total = A_circle + A_square
A_total = 100π + 144 square yards.Therefore, the equation for the area of the compound shape would be A = 100π + 144 square yards.