hello! i need some help, i'm doing a pythagorean theorem problem and im stuck on one of the quadrilaterals.
i'll try to describe it as i cant show pictures.
Use the Pythagorean Theorem to find the area of Field C in acres
Field C is a rhombus with points at (4,7), (7,3) (3,0) and (0,4)
To find the area of Field C, we first need to calculate the lengths of its diagonals.
The diagonal lengths of a rhombus are equal and can be found using the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the lengths of both diagonals:
Length of diagonal AC:
d1 = √((7 - 4)^2 + (3 - 7)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5
Length of diagonal BD:
d2 = √((0 - 3)^2 + (4 - 0)^2) = √((-3)^2 + 4^2) = √(9 + 16) = √25 = 5
Now that we have the lengths of the diagonals, we can use the Pythagorean Theorem to find the length of one side of the rhombus:
s = √((d1/2)^2 + (d2/2)^2)
= √((5/2)^2 + (5/2)^2)
= √(25/4 + 25/4)
= √(25/2)
= 5/√2
The area of a rhombus can be found using the formula:
Area = (diagonal 1 * diagonal 2) / 2
Let's substitute the values:
Area = (d1 * d2) / 2
= (5 * 5) / 2
= 25 / 2
= 12.5 acres
So, the area of Field C is 12.5 acres.