Question

An artist is painting the front of a picture frame. What is the area of the frame? Assume that all segments that look congruent and all angles that look like right angles are right angles. (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

In order to find the area of the frame, we need to know the dimensions of the frame and the width of the painted area on the front of the frame.

Let's assume the dimensions of the frame are: length = L and width = W.

If the artist is painting the front of the frame, we can assume that the width of the painted area is x. Therefore, the dimensions of the inner rectangle (unpainted area) would be (L-2x) and (W-2x).

The area of the unpainted inner rectangle is:
Area = (L-2x)(W-2x)

And the area of the whole frame (painted area + unpainted area) is:
Area = LW

We are looking for the area of the frame, which is the area of the whole frame minus the area of the unpainted inner rectangle:
Area of frame = (LW) - (L-2x)(W-2x)

Using FOIL (First, Outer, Inner, Last) method:
Area of frame = LW - LW - 2xW - 2xL + 4x^2
Area of frame = - 2xW - 2xL + 4x^2

Therefore, the area of the frame is - 2xW - 2xL + 4x^2.