Question

This shows the template for a diamond-shaped mirror frame. (View attachment)

Answer 1

Answer:

We know that the area of a square of side length L is given by:

A = L^2

Here, the total area of the white square is:

A = (3x + 1)^2

And the area of the shaded square is:

A' = (2x + 3)^2

a) If we remove the shaded area from the white area, the remaining area is just the difference between the two, then:

area = A - A' =  (3x + 1)^2 - (2x + 3)^2

This is the expression we wanted.

b) Now we need to expand and simplify the expression:

area = (3x + 1)^2 - (2x + 3)^2

area = (3x)^2 + 2*(3x)*1 + 1^2 - (2x)^2 - 2*(2x)*3 - 3^2

area = 9x^2 + 6x + 1 - 4x^2 - 12x - 9

area = (9 - 4)*x^2 + (6 - 12)*x + 1 - 9

area = 5*x^2 - 6*x - 8

This is the simplified equation for the remaining area.