Find the area of rectangle ABCD that has vertices point A (2,−5) , point B (5,−5) , point C (5,−1) , and point D (2,−1) in square miles.
To find the area of the rectangle, we can use the formula for the area of a rectangle:
Area = Length x Width
First, we need to calculate the length and width of the rectangle. The length is the distance between points A and B, and the width is the distance between points B and C.
Using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Length = √((5 -2)^2 + (-5 - (-5))^2) = √(3^2 + 0^2) = √9 = 3 miles
Width = √((5 -2)^2 + (-1 - (-5))^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 miles
Now, we can find the area:
Area = 3 miles x 5 miles = 15 square miles
Therefore, the area of rectangle ABCD is 15 square miles.
wrong
I apologize for the mistake. Let's try again.
Given the coordinates of the vertices of the rectangle:
A (2, -5)
B (5, -5)
C (5, -1)
D (2, -1)
We first need to calculate the length and width of the rectangle.
Length = Distance between points A and B = 5 - 2 = 3 miles
Width = Distance between points B and C = -1 - (-5) = 4 miles
Now, we can find the area of the rectangle:
Area = Length x Width
Area = 3 miles x 4 miles
Area = 12 square miles
Therefore, the correct area of rectangle ABCD is 12 square miles. Thank you for your patience.
nahuh
Let's calculate the area correctly this time.
To find the area of the rectangle with vertices A(2,-5), B(5,-5), C(5,-1), and D(2,-1), we need to calculate the length and width of the rectangle.
The length of the rectangle AB (or DC) can be calculated as the difference between the x-coordinates of points A and B:
Length = 5 - 2 = 3 miles
The width of the rectangle BC (or AD) can be calculated as the difference between the y-coordinates of points B and C:
Width = -1 - (-5) = 4 miles
Now, we can find the area of the rectangle by multiplying the length and width:
Area = Length x Width
Area = 3 miles x 4 miles
Area = 12 square miles
Therefore, the area of the rectangle ABCD is 12 square miles. Thank you for your patience.