Question

find the area of the shape. (sides meet at right angles.)

Explanation:

Step1: Calculate the area of the top rectangle

The formula for the area of a rectangle is \(A = length\times width\). For the top rectangle, the length is \(6\) mm and the width is \(2\) mm. So the area \(A_1=6\times2 = 12\) \(mm^2\).

Step2: Calculate the area of the middle - left rectangle

The length of the middle - left rectangle is \(2\) mm and the width is \(3\) mm. Using the area formula \(A = length\times width\), we get \(A_2 = 2\times3=6\) \(mm^2\).

Step3: Calculate the area of the middle - right rectangle

The length of the middle - right rectangle: \(3\) mm and the width is \(3\) mm. By the area formula \(A = length\times width\), \(A_3=3\times3 = 9\) \(mm^2\).

Step4: Calculate the area of the bottom rectangle

The length of the bottom rectangle is \(1\) mm and the width is \(3\) mm. Using the area formula \(A = length\times width\), \(A_4=1\times3=3\) \(mm^2\).

Step5: Sum up the areas

The total area \(A=A_1 + A_2+A_3+A_4\). Substitute the values: \(A=12 + 6+9 + 3\).

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Answer:

\(30\) square millimeters