Finding the Area of a Field

Question

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

Answer 1

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.