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=(1)/(2)(3)(4)=6\\\\A_2=(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`