Question

which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)? (1 point) (9 + 6) · (9 + 11) 9 · 6 · 11 11 (6 + 9) (9 · 6) + (9 · 11)

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $A = l\times w$. The large rectangle is composed of two smaller rectangles with the same height of 9. The widths of the two smaller rectangles are 6 and 11 respectively.

Step2: Calculate area of each small rectangle

The area of the first small - rectangle with width 6 and height 9 is $A_1=9\times6$. The area of the second small - rectangle with width 11 and height 9 is $A_2 = 9\times11$.

Step3: Use distributive property for total area

The area of the entire rectangle $A=A_1 + A_2$. By the distributive property $a\times(b + c)=a\times b+a\times c$, here $a = 9$, $b = 6$, $c = 11$, so $A=(9\times6)+(9\times11)$.

Answer:

$(9\times6)+(9\times11)$