Question

what is the area of this figure?
write your answer using decimals, if
necessary.
square millimeters

Explanation:

Step1: Calculate the area of the rectangle on the left

The rectangle on the left has a width of \(3 + 3=6\) mm and a height of \(2\) mm.
The area of a rectangle is \(A = length\times width\), so \(A_1=2\times6 = 12\) \(mm^2\)

Step2: Calculate the area of the middle rectangle

The middle rectangle has a length of \(7\) mm and a height of \(4-(2) = 2\) mm.
Using the formula \(A = length\times width\), \(A_2=7\times2=14\) \(mm^2\)

Step3: Calculate the area of the trapezoid on the right

The trapezoid has bases \(b_1 = 7 + 2+4=13\) mm and \(b_2=7 + 2=9\) mm, and height \(h = 4\) mm.
The area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), so \(A_3=\frac{(13 + 9)\times4}{2}=\frac{22\times4}{2}=44\) \(mm^2\)

Step4: Sum up the areas

Add the areas of the three parts: \(A = A_1+A_2+A_3\)
\(A=12 + 14+44\)

Answer:

\(70\)