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

Answer 1

To find the area of rectangle ABCD, we can use the coordinates of its vertices: A(1, 7), B(3, 7), C(3, -4), and D(1, -4).

1. Calculate the lengths of the sides:

   • The length of side AB (which is horizontal) can be calculated as the difference between the x-coordinates of A and B: \[ AB = |x_B - x_A| = |3 - 1| = 2 \]

   • The length of side AD (which is vertical) can be calculated as the difference between the y-coordinates of A and D: \[ AD = |y_A - y_D| = |7 - (-4)| = |7 + 4| = 11 \]

2. Calculate the area of the rectangle:

   • The area \(A\) of a rectangle is given by the formula: \[ A = \text{length} \times \text{width} \]
   • Using the lengths calculated: \[ A = AB \times AD = 2 \times 11 = 22 \]

Thus, the area of rectangle ABCD is \(\boxed{22}\).