Use the Pythagorean theorem to find the area of field C in acres (4,7) (0,4) (3,0) (7,3)

Answer 1

To find the area of field C, we can divide it into two triangles.

First, we need to find the length of one side of each triangle.

For the first triangle, we can use the points (4, 7), (0, 4), and (3, 0) to form a right triangle. The length of the base is 4 - 0 = 4 units, and the length of the height is 7 - 0 = 7 units.

Using the Pythagorean theorem, we have:
hypotenuse^2 = base^2 + height^2.
hypotenuse^2 = 4^2 + 7^2.
hypotenuse^2 = 16 + 49.
hypotenuse^2 = 65.

To simplify the calculation of area, let's take the square root of both sides:
hypotenuse = √65.

The area of the triangle is given by:
area1 = 1/2 * base * height.
area1 = 1/2 * 4 * 7.
area1 = 14 square units.

For the second triangle, we can use the points (3, 0), (7, 3), and (4, 7) to form another right triangle. The length of the base is 7 - 3 = 4 units, and the length of the height is 7 - 0 = 7 units.

Again, using the Pythagorean theorem, we have:
hypotenuse^2 = base^2 + height^2.
hypotenuse^2 = 4^2 + 7^2.
hypotenuse^2 = 16 + 49.
hypotenuse^2 = 65.

Taking the square root of both sides:
hypotenuse = √65.

The area of the second triangle is:
area2 = 1/2 * base * height.
area2 = 1/2 * 4 * 7.
area2 = 14 square units.

Finally, to find the total area of field C, we sum the areas of both triangles:
total area = area1 + area2.
total area = 14 + 14.
total area = 28 square units.

Now, to convert the area from square units to acres, we need to divide by the conversion factor. Since 1 acre is equal to 43,560 square feet, we have:
total area in acres = 28 / 43,560.
total area in acres ≈ 0.0006432714740207 acres.

Therefore, the area of field C is approximately 0.0006 acres.