Question

A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.

On a coordinate plane, 2 squares are shown. The photograph has points (negative 3, negative 2), (negative 2, 2), (2, 1), and (1, negative 3). The red paper has points (negative 4, 4), (4, 4), (4, negative 4), and (negative 4, negative 4).

What is the area of the piece of red paper after the hole for the photograph has been cut?

17 square units
25 square units
39 square units
47 square units

Answer 1

Big red square side length = 8 (from x = -4 to 4), so area = 8^2 = 64.

Area of the photograph (polygon with vertices (-3,-2), (-2,2), (2,1), (1,-3)) by the shoelace formula:

Sum1 = (-3)(2)+(-2)(1)+(2)(-3)+(1)(-2) = -6-2-6-2 = -16
Sum2 = (-2)(-2)+(2)(2)+(1)(1)+(-3)(-3) = 4+4+1+9 = 18
Area = 1/2 |Sum1 - Sum2| = 1/2 | -16 - 18 | = 17.

Remaining red area = 64 - 17 = 47 square units.

Answer: 47 square units.