Question

Maria is framing an 8 inch by 10 inch photograph with matting as shown. Which is an expression for the area of the photograph with the mat?

Answer 1

`4x^2 + 36x + 80`

Explanation:

Area of the photograph with the mat = area of the photograph + area of the mat

Area of the photograph = length * width = 10*8 = 80 in²

Area of the mat:

Decompose the mat frame into 4 rectangles and 4 squares (these are the corners of x*x dimensions)

The 4 rectangles = 2(8*x) + 2(10*x) = 16x + 20x = 36x

The 4 squares (the corners) = 4(x*x) = 4x²

The area of the photograph with the mat = 80 + 36x + 4x²

Rearrange in standard form:

The expression for the area would be:

✅
`4x^2 + 36x + 80`