Write an expression for the missing dimension of each shaded

Write an expression for the missing dimension of each shaded figure and a multiplication expression for its area. Then expand and simplify the multiplication expression.

Solution

the total side length is =14

let us say the the small part side length is a (unknown)

now 14 = a + (x-3)

a = 14-3 -x

a = 11 -x

the area = 12(11 -x) [ for the highlighted rectangle]

= 12*11 - 12x

= 131 -12x