Question

each square in the figure below has an area of 1 square unit. we can break the figure into two parts. complete the equations to find the area of the entire figure.

Explanation:

Step1: Calculate the area of the first part

The first part is a rectangle with length \(6\) and width \(4\). The area of a rectangle is \(A = length\times width\), so \(A_1=6\times4 = 24\)

Step2: Calculate the area of the second part

The second part is a rectangle with length \(2\) and width \(4\). Using the area formula \(A = length\times width\), we get \(A_2=2\times4=8\)

Step3: Calculate the total area

The total area \(A = A_1 + A_2\). Substitute \(A_1 = 24\) and \(A_2=8\) into the formula, \(A=24 + 8=32\)

Another way:

Step1: Consider the whole figure as a rectangle

The whole figure has length \(8\) (\(6 + 2\)) and width \(4\). Using the area formula \(A=length\times width\), \(A=(6 + 2)\times4\)

Step2: Expand the formula

Using the distributive property \(a\times(b + c)=a\times b+a\times c\), here \(a = 4\), \(b = 6\), \(c = 2\). So \(A=4\times6+4\times2\)

Step3: Calculate the values

\(4\times6 = 24\) and \(4\times2=8\). Then \(A=24 + 8=32\)

Answer:

The equations can be \(4\times6+4\times2 = 32\) or \(4\times(6 + 2)=32\)