Question

Find the area of rectangle ABCD , with vertices A(1,7) , B(3,7) , C(3,−4) , and D(1,−4) .(1 point)
units2

Answer 1

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.