1. Count the number of squares that make one side of Field A.

Question

Side length = 4 acres (worth 2 points)

2. Count the number of squares that make one side of Field B.

Side length = 3 acres (worth 2 points)

3. Use the Pythagorean Theorem to find the area of Field C in acres:

Area: a² + b² = c2

Hint: You can either square your side lengths when simplifying a² and b², or you can count the squares in each of those fields for the same value.

Area of Field C = blank acres

Answer 1

To solve the problem, we will follow the steps outlined in your questions.

1. For Field A with a side length of 4 acres:

   • Since each square is 1 acre, the number of squares that make up one side of Field A is simply 4 acres.
   • Thus, for Field A: 4 squares (worth 2 points).

2. For Field B with a side length of 3 acres:

   • Since each square is 1 acre, the number of squares that make up one side of Field B is 3 acres.
   • Thus, for Field B: 3 squares (worth 2 points).

3. To find the area of Field C using the Pythagorean Theorem, we first assume the side lengths represent a right triangle, where:

   • a = side of Field A = 4 acres
   • b = side of Field B = 3 acres

   According to the Pythagorean Theorem: \[ c^2 = a^2 + b^2 \] Plugging the values into the equation: \[ c^2 = 4^2 + 3^2 \] \[ c^2 = 16 + 9 \] \[ c^2 = 25 \]

   To find c: \[ c = \sqrt{25} = 5 \]

The area of Field C can be represented as square acres, since it denotes the length of the hypotenuse of the triangle in this context:

• So, the area of Field C = 5 acres.

Thus, the answers are:

1. 4 squares for Field A
2. 3 squares for Field B
3. Area of Field C = 5 acres