Answer:
3.44
Step-by-step explanation:
To find the area of the leftover poster board, we first need to determine the area of the original square poster board and then subtract the area of the four circles that Anna has cut out.
The area of a square is given by the formula:
Area = side_length^2
Since the circles are cut from a square piece of poster board, all four circles are of equal size and their diameters are the same as the side length of the square. Let's denote the side length of the square as "a" and the diameter of a circle as "d". We know that:
d = a
Now, let's calculate the area of one circle using the formula:
Area_of_circle = π * r^2
where r is the radius of the circle, and we are given that r = d/2 = a/2.
Area_of_circle = π * (a/2)^2 = π * a^2 / 4
Since there are four circles, the total area of the circles cut out is:
Total_area_of_circles = 4 * Area_of_circle = 4 * (π * a^2 / 4) = π * a^2
Now, we can find the area of the leftover poster board by subtracting the total area of the circles from the area of the original square:
Leftover_area = Area - Total_area_of_circles = a^2 - π * a^2
However, we cannot determine the exact side length "a" from the information provided. Let's assume that Anna cut the circles carefully and the leftover piece has a very small area compared to the original square. In this case, we can approximate the side length "a" as the diameter of one circle:
a ≈ d = 4 ft (since the diameter of one circle is the same as the side length of the square)
Now, we can calculate the approximate area of the leftover poster board:
Leftover_area ≈ (4 ft)^2 - π * (4 ft)^2 ≈ 16 sq.ft - 12.56 sq.ft ≈ 3.44 sq.ft
Therefore, the approximate area of the leftover poster board is 3.44 square feet.