Question

which expression below does not give the area of this figure? figure: two adjacent rectangles, left with width ( a ) and height ( c ), right with width ( b ) and height ( c ). options: ( ac + bc ), ( ab + ac ), ( c(a + b) ), ( (a + b)c )

Explanation:

Step1: Analyze the figure's area

The figure is a rectangle composed of two smaller rectangles. The total length is \(a + b\) and the height is \(c\), so the area can be calculated as \((a + b)c\) or \(c(a + b)\) (by the distributive property, this is also \(ac + bc\)).

Step2: Evaluate each expression

• \(ac + bc\): This is the sum of the areas of the two smaller rectangles (area of first: \(a\times c = ac\), area of second: \(b\times c = bc\)), so it gives the total area.
• \(ab + ac\): The term \(ab\) does not represent the area of any part of the figure (the sides are \(a, b, c\), and the areas of the parts are \(ac\) and \(bc\)), so this expression does not give the area.
• \(c(a + b)\): By the distributive property, \(c(a + b)=ac + bc\), which is the total area.
• \((a + b)c\): This is the same as \(c(a + b)\) (multiplication is commutative), so it gives the total area.

Answer:

\(ab + ac\) (the second option, \(ab + ac\))