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.
Count the number of squares inside Field A. This is the area of Field A in acres. Write it on your worksheet.
Count the number of squares inside Field B. This is the area of Field B in acres. Write it on your worksheet.
Use the Pythagorean Theorem to find the area of Field C in acres.
To find the size of Field C, we need to find the area in acres.
Let's first count the number of squares inside Field A. From the given diagram, it seems like Field A consists of 9 squares. So, the area of Field A is 9 acres.
Next, let's count the number of squares inside Field B. From the diagram, it looks like Field B consists of 16 squares. So, the area of Field B is 16 acres.
To find the area of Field C, we need to use the Pythagorean Theorem. Let's say Field C is a square field.
Since Field C is formed by combining Field A and Field B, the area of Field C can be found by adding the areas of Field A and Field B.
Area of Field C = Area of Field A + Area of Field B
Area of Field C = 9 acres + 16 acres
Area of Field C = 25 acres
So, the area of Field C is 25 acres.
To find the area of Field A, count the number of squares inside it. Let's say there are 6 squares inside Field A. Therefore, the area of Field A is 6 acres.
To find the area of Field B, count the number of squares inside it. Let's say there are 4 squares inside Field B. Therefore, the area of Field B is 4 acres.
Now, to find the area of Field C, we can use the Pythagorean Theorem. However, we need some additional information such as the lengths of the sides of Field C. Please provide the necessary measurements so that we can proceed with calculating the area of Field C.
To find the area of Field C, you need to count the number of squares in Field A and Field B first, then use the Pythagorean theorem.
Here are the steps to find the areas:
1. Count the number of squares inside Field A and write it on your worksheet. Let's say there are 5 squares inside Field A.
2. Count the number of squares inside Field B and write it on your worksheet. Let's say there are 8 squares inside Field B.
3. Add the number of squares in Field A and Field B together: 5 squares (Field A) + 8 squares (Field B) = 13 squares.
4. Use the Pythagorean theorem to find the area of Field C. The Pythagorean theorem states that 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 A and Field B form a right triangle, and the hypotenuse is the diagonal side of Field C.
Let's assume that the length of one side of a square is y yards (since 1 acre is equal to 4,840 square yards). The diagonal of each square (and the hypotenuse of Field C) would be the square root of 2 times the length of one side (y).
Therefore, the length of the hypotenuse (Field C) will be the square root of 2y.
5. Square the length of the hypotenuse to find the area of Field C: (sqrt(2y))^2 = 2y.
So the area of Field C in acres would be 2 times the total number of squares (from step 3), since each square represents one acre.
For example, if there are 13 squares, then the area of Field C would be 2 x 13 = 26 acres.
Remember to write the area of Field C in acres on your worksheet.