Farmers need to know the area of their land in order to plan for growing their crops.
Farmers measure the size of their fields in acres. One acre is equal to 4,840 square yards. In the diagram on the worksheet, each of the squares in the grid represents one acre. Count the number of acres inside Fields A and B to find their measure, and then use that information to find the size of Field C.
1. Count the number of squares inside Field A. This is the area of Field A in acres.
Write it on your worksheet.
2. Count the number of squares inside Field B. This is the area of Field B in acres.
Write it on your worksheet.
3. Use the Pythagorean Theorem to find the area of Field C in acres.
To find the area of Field C, we need to use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c).
Therefore, we can use this theorem to find the length of the hypotenuse of Field C, which will give us the number of squares inside Field C.
Let's assume that the length of one side of the square grid is x.
In Field A, we counted a total of n squares, so the length of one side of Field A is √n.
In Field B, we counted a total of m squares, so the length of one side of Field B is √m.
Using the Pythagorean Theorem, we can set up the following equation:
(x^2 + (√n)^2) + (x^2 + (√m)^2) = (2x)^2
Simplifying the equation, we get:
x^2 + n + x^2 + m = 4x^2
2x^2 + n + m = 4x^2
Combining like terms, we get:
2x^2 - 4x^2 = -n - m
-2x^2 = -n - m
Dividing both sides by -2, we get:
x^2 = (n + m)/2
Taking the square root of both sides, we get:
x = √((n + m)/2)
Now that we have the length of one side of the square grid, we can find the area of Field C.
The area of Field C is the total number of squares inside Field C, which is equal to the length of one side of the square grid squared.
Therefore, the area of Field C in acres is (√((n + m)/2))^2.
Write the area of Field C on your worksheet.
Give answer in each question like 1. 2. 3.
1. Count the number of squares inside Field A. This is the area of Field A in acres. Answer: __________ acres.
2. Count the number of squares inside Field B. This is the area of Field B in acres. Answer: __________ acres.
3. Use the Pythagorean Theorem to find the area of Field C in acres. Answer: __________ acres.
To find the area of Field C, we will use the Pythagorean Theorem. The Pythagorean Theorem states that in a right 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.
In this case, Field C forms a right triangle. The two sides adjacent to the right angle can be found by counting the number of squares horizontally and vertically. Let's call these sides "a" and "b".
So, to find the area of Field C in acres, we can follow these steps:
1. Count the number of squares along each side of Field C. Let's say side "a" has x squares and side "b" has y squares.
2. Use the Pythagorean Theorem: a^2 + b^2 = c^2, where "c" represents the hypotenuse.
3. Calculate the value of "c^2" by substituting the values of "a" and "b" into the equation: (x^2) + (y^2) = c^2.
4. Take the square root of the value obtained in step 3 to find the length of the hypotenuse "c".
5. Finally, because each square in the grid represents one acre, you can use the area of a triangle formula (A = 0.5 * base * height) to find the area of Field C.
6. Substitute the length of the hypotenuse "c" obtained in step 4 as the base or height in the formula, depending on how you choose to calculate. Multiply by 0.5, and you will get the area of Field C in acres.
Remember to write the results on your worksheet for Field A, Field B, and the calculated area of Field C.