Finding the Area of a Field
Use the image to answer to complete the activity.
Finding the Area of a Field
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 Square A in acres. Write it below: (1 point)
Area = __________ acres
Count the number of squares inside Field B. This is the area of Square B in acres. Write it below: (1 point)
Area = __________ acres
3. SHOW YOUR WORK: Use the Pythagorean Theorem to find the area of Field C in acres: (2 points)
Area = __________ acres
1. The number of squares inside Field A is 4.
Area = 4 acres
2. The number of squares inside Field B is 5.
Area = 5 acres
3. Field C is a right triangle. The lengths of the two legs are 3 squares and 4 squares respectively.
Using the Pythagorean Theorem, the length of the hypotenuse (the diagonal of the triangle) is √(3^2 + 4^2) = √(9 + 16) = √25 = 5 squares.
Since each square represents 1 acre, the area of Field C is 5 acres.
To answer the questions step-by-step:
1. Count the number of squares inside Field A:
Area = 10 squares
2. Count the number of squares inside Field B:
Area = 15 squares
3. To find the area of Field C using the Pythagorean Theorem, we need to find the length of Side C.
a. From the diagram, we can see that Side A has a length of 5 squares and Side B has a length of 8 squares.
b. Use the Pythagorean Theorem:
c^2 = a^2 + b^2
c^2 = 5^2 + 8^2
c^2 = 25 + 64
c^2 = 89
c ≈ √89
4. Now, we can find the area of Field C by multiplying the length of Side C by the length of Side C:
Area = (√89) * (√89)
Area ≈ 89 acres
To find the area of Field A, we need to count the number of squares inside Field A. Each square represents one acre. So, we just need to count the squares and write it as the area in acres.
To find the area of Field B, we need to count the number of squares inside Field B. Each square represents one acre. So, we just need to count the squares and write it as the area in acres.
Now, to find the area of Field C, we are asked to 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 the diagram, we can see that Field C is a right triangle. One side of the triangle is the length of Field A (which we found earlier), and the other side is the length of Field B (which we also found earlier).
To find the length of Field C, we can use the Pythagorean Theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (Field C), and a and b are the lengths of the other two sides (Field A and Field B).
Once we find c, we can find the area of Field C by counting the squares inside Field C. Each square represents one acre, so we just need to count the squares and write it as the area in acres.