Find the area of rectangle ABCD with vertices A(1,7),b(3,7),c(3,-4)d(1,-4)

Answer 1

To find the area of a rectangle with the given vertices, we can use the formula for the area of a rectangle which is given by the product of its length and width.

First, we need to find the length and width of the rectangle. The length of the rectangle can be found by finding the distance between points A(1,7) and B(3,7) using the distance formula:

Length = √((3-1)^2 + (7-7)^2)
Length = √(2^2 + 0^2)
Length = √4
Length = 2

Similarly, the width of the rectangle can be found by finding the distance between points B(3,7) and C(3,-4):

Width = √((3-3)^2 + (7-(-4))^2)
Width = √(0^2 + 11^2)
Width = √121
Width = 11

Now, we can calculate the area of the rectangle by multiplying the length and width:

Area = Length x Width
Area = 2 x 11
Area = 22

Therefore, the area of rectangle ABCD with vertices A(1,7), B(3,7), C(3,-4), and D(1,-4) is 22 square units.