Question

Rectangle ABCD has vertices A(-3, 1), B(5, 7), C(9, 4), and D(1, -2). Calculate the
area of rectangle ABCD.

Answer 1

It's not a rectangle. Look at the picture.

It is a parallelogram.

The area of the red rectangle:

$A_{\boxed{ \ }}=(4+8)(6+3)=(12)(9)=108$

The areas of the right triangles:

$A_1=\dfrac{1}{2}(3)(4)=6\\\\A_2=\dfrac{1}{2}(6)(8)=24$

The area of a parallelogram:

$A=A_{\boxed{ \ }}-(2A_1+2A_2)\\\\A=108-(2\cdot6+2\cdot24)=108-(12+48)=108-60=48$