Question

Sasha cuts four identical circles from a square piece

of black poster board as shown
What is the area of the leftover poster board?
Use 3.14 for
1.935 square feet
7.065 square feet
4.935 square feet
7.234 square feet

Answer 1

The area of the leftover poster board is 1.935
`ft^(2)`

Explanation:

In this question, we are tasked with calculating the area of the left-over poster board.

To calculate the area of this left over, what we need to do is to subtract the areas of the 4 circles summed together from the area of the square.

The length of a side of the square is 3 ft, this means that the area of the square which is mathematically equal to
`S^(2)` is
`3^(2)` = 9
`ft^(2)`

Each of the circles are similar and identical and have a diameter of 1.5 ft each. This is because, for the two circles on each side, the total length running through their middle is 3 ft and thus, each will have an individual length of 1.5 ft as diameter(measurement from the top of the circle to the bottom through the center of the circles)

Now, since the diameter of the circle is 1.5, the radius is half the diameter which is 1.5/2 = 0.75 ft

Mathematically, the area of a circle can be calculated using the formula π×
`r^(2)`.

Since we are having 4 identical circles area, the formula becomes 4 × π×
`r^(2)`

for the total of the 4 circles

Using the radius of 0.75 ft , the total area becomes; 4 ×3.14×
`0.75^(2)` = 7.065
`ft^(2)`

The area of the leftover poster board = Area of the square - Area of the 4 circles = (9 - 7.065)
`ft^(2)` = 1.935
`ft^(2)`