Find the area of rectangle ABCD , with vertices A(1,7) , B(3,7) , C(3,−4) , and D(1,−4) .(1 point)
units2
To find the area of a rectangle with these coordinates, we can first calculate the length of the base and the height of the rectangle.
The base of the rectangle can be calculated by finding the distance between points A and B:
Base AB = √[(3-1)^2 + (7-7)^2] = √[2^2 + 0^2] = √4 = 2 units
The height of the rectangle can be calculated by finding the distance between points A and D:
Height AD = √[(1-1)^2 + (7-(-4))^2] = √[0^2 + 11^2] = √121 = 11 units
Therefore, the area of rectangle ABCD can be calculated by multiplying the base and the height:
Area = base x height
Area = 2 units x 11 units
Area = 22 square units
So, the area of rectangle ABCD is 22 square units.