Question

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 \(\boxed{22}\).