9. 3.5 cm 4.0 cm 6.3 cm 9.1 cm

Response

Step 1: Divide the figure into two rectangles
We can divide the given composite - shaped figure into two rectangles. One rectangle has dimensions \(4.0\ cm\times6.3\ cm\) and the other rectangle has dimensions \((9.1 - 4.0)\ cm\times(6.3 - 3.5)\ cm\).
Step 2: Calculate the area of the first rectangle
The area formula for a rectangle is \(A = l\times w\). For the first rectangle with length \(l_1=4.0\ cm\) and width \(w_1 = 6.3\ cm\), the area \(A_1=l_1\times w_1=4.0\times6.3 = 25.2\ cm^{2}\).
Step 3: Calculate the dimensions of the second rectangle
The length of the second rectangle \(l_2=9.1 - 4.0=5.1\ cm\), and the width \(w_2=6.3 - 3.5 = 2.8\ cm\).
Step 4: Calculate the area of the second rectangle
Using the area formula \(A = l\times w\), for the second rectangle, \(A_2=l_2\times w_2=5.1\times2.8 = 14.28\ cm^{2}\).
Step 5: Calculate the total area of the figure
The total area \(A = A_1+A_2\). So \(A=25.2 + 14.28=39.48\ cm^{2}\).

Step 1: Divide the figure into two rectangles
We can divide the given composite - shaped figure into two rectangles. One rectangle has dimensions \(4.0\ cm\times6.3\ cm\) and the other rectangle has dimensions \((9.1 - 4.0)\ cm\times(6.3 - 3.5)\ cm\).
Step 2: Calculate the area of the first rectangle
The area formula for a rectangle is \(A = l\times w\). For the first rectangle with length \(l_1=4.0\ cm\) and width \(w_1 = 6.3\ cm\), the area \(A_1=l_1\times w_1=4.0\times6.3 = 25.2\ cm^{2}\).
Step 3: Calculate the dimensions of the second rectangle
The length of the second rectangle \(l_2=9.1 - 4.0=5.1\ cm\), and the width \(w_2=6.3 - 3.5 = 2.8\ cm\).
Step 4: Calculate the area of the second rectangle
Using the area formula \(A = l\times w\), for the second rectangle, \(A_2=l_2\times w_2=5.1\times2.8 = 14.28\ cm^{2}\).
Step 5: Calculate the total area of the figure
The total area \(A = A_1+A_2\). So \(A=25.2 + 14.28=39.48\ cm^{2}\).