1. Count the number of squares inside Field A. This is the area of Square A in acres. Write it below: (1 point)
Area = _____16____ acres
2. Count the number of squares inside Field B. This is the area of Square B in acres. Write it below: (1 point)
Area = ______9____ acres
3. SHOW YOUR WORK: Use the Pythagorean Theorem to find the area of Field C in acres: (2 points)
Area = ________ acres
4. Add your answers from 1 and 2 then compare the result with your answer to 3. How do they compare? (1 point)
3. SHOW YOUR WORK:
Using the Pythagorean Theorem, we can find the length of one side of Square C.
Let's call the length of one side of Square C "x".
The diagonal of Square C is 20 meters.
Using the Pythagorean Theorem, we have:
x^2 + x^2 = 20^2
2x^2 = 400
x^2 = 200
x = √200
x ≈ 14.14
The area of Square C is given by x^2:
Area = (14.14)^2
Area ≈ 200 acres
4. The areas of Square A and Square B are 16 acres and 9 acres respectively. The sum of these areas is 16 + 9 = 25 acres. This is less than the area of Square C which is approximately 200 acres.
THAT MAKES NO SENCE I NEED YOU TO USE 16 A AND B 9 THE Pythagorean Theorem to find the area of Field C in acres THEN YOU . Add your answers from 1 and 2 then compare the result with your answer to 3. How do they compare?
I apologize for the confusion. Let's do the calculation again using the given values.
1. The number of squares inside Field A is 16.
Area of Square A = 16 acres.
2. The number of squares inside Field B is 9.
Area of Square B = 9 acres.
3. Let's find the area of Field C using the Pythagorean Theorem.
In Square C, one side is the hypotenuse and the other two sides are equal.
Let's call the length of one side of Square C "x".
Using the Pythagorean theorem, we have:
x^2 + x^2 = (20)^2
2x^2 = 400
x^2 = 200
x = √200
The area of Square C is given by x^2:
Area of Square C ≈ (√200)^2 ≈ 200 acres.
4. The sum of the areas of Square A and Square B is:
16 + 9 = 25 acres.
Comparing this with the area of Square C (which is approximately 200 acres), we can see that the sum of the areas of Square A and Square B (25 acres) is significantly smaller than the area of Square C.
1. To count the number of squares inside Field A, you would need to visually count all the squares. Once you have counted them, you can write down the total number of squares counted in the given space. In this case, the answer is 16 squares.
2. Similar to Field A, for Field B, you would need to visually count the number of squares inside it. Once you have counted them, you can write down the total number of squares counted in the given space. In this case, the answer is 9 squares.
3. The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
To find the area of Field C, we need to use the Pythagorean Theorem. However, since we are given squares in this case, we can use a simplified version of the theorem. Since the sides of a square are equal, we only need to find the length of one side.
Let's assume one side of the square in Field C is 'x.' According to the theorem, the diagonal (hypotenuse) of the square is the square root of two times the side. So, the equation becomes:
diagonal = sqrt(2x)
We are asked for the area, so we need to square the side length. Thus, the area is:
Area = x^2
Now, we can replace the value of x with sqrt(2x) from the previous equation:
Area = (sqrt(2x))^2
Simplifying the expression:
Area = 2x
So the area of Field C in acres is 2 times the length of one side of the square.
4. To compare the answers from the previous questions, we add the areas from Field A and Field B, which are 16 and 9 acres, respectively:
16 acres + 9 acres = 25 acres
Then, we compare this sum (25 acres) with the answer from question 3. If the areas are equal, they should both be 25 acres. If they are not, there may be an error in the calculations or measurements. You can write down how the results compare, such as "The sum of areas 1 and 2 is equal to the area in question 3" or "The sum of areas 1 and 2 is not equal to the area in question 3."