To find the area of Field C, we need to first calculate the length of one side of the field.
Using the Pythagorean Theorem, the length of one side (A) can be calculated as follows:
A = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates (4, 7) and (7, 3), we can calculate A:
A = √((7 - 4)^2 + (3 - 7)^2)
= √(3^2 + (-4)^2)
= √(9 + 16)
= √25
= 5
Therefore, the length of one side of Field C is 5.
Now, to find the area of the field (C), we need to calculate the product of the lengths of two sides (A and B) of the field.
Using the coordinates (4, 7) and (0, 4), we can calculate B:
B = √((0 - 4)^2 + (4 - 7)^2)
= √((-4)^2 + (-3)^2)
= √(16 + 9)
= √25
= 5
Therefore, the length of the other side (B) of Field C is also 5.
The area (A) of the field is calculated by multiplying the lengths of the two sides:
Area = A * B
= 5 * 5
= 25
Since 1 acre is equal to 43,560 square feet, we need to convert the area to acres:
Area in acres = Area / 43,560
= 25 / 43,560
≈ 0.00057 acres
Therefore, the area of Field C is approximately 0.00057 acres.
Use the Pythagorean Theorem to find the area of Field C in acres
(4, 7)
(7, 3)
(0, 4)
(3, 0)
1 answer