To find the area of Field C, we need to determine the length of each side of the field using the given coordinates and then use the Pythagorean Theorem to calculate the area.
First, we find the length of the horizontal side of the field by subtracting the x-coordinates of the two given points on the line: 7 - 4 = 3.
Next, we find the length of the vertical side of the field by subtracting the y-coordinates of the two given points on the line: 7 - 3 = 4.
We can now use the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the two sides are the horizontal side with a length of 3 and the vertical side with a length of 4. The hypotenuse is the diagonal of the field.
Using the Pythagorean Theorem, we can calculate the length of the diagonal:
Diagonal² = Horizontal side² + Vertical side²
Diagonal² = 3² + 4²
Diagonal² = 9 + 16
Diagonal² = 25
Diagonal = √25
Diagonal = 5
Now that we know the length of the diagonal, we can find the area of the field. The area of a right triangle is calculated by multiplying its two shorter sides and then dividing the result by 2.
Area = (Horizontal side * Vertical side) / 2
Area = (3 * 4) / 2
Area = 12 / 2
Area = 6 acres
Therefore, the area of Field C is 6 acres.
Use the Pythagorean Theorem to find the area of Field C in acres
(4,7)
(7,3)
(0,4)
(3,0)
1 answer