Question

what is the area of this figure?

Explanation:

Step1: Divide the figure into simpler shapes

Divide the figure into a trapezoid, two rectangles.

Step2: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\). Here, \(a = 4\) mm, \(b=5 + 4=9\) mm, \(h = 6\) mm.
\(A_1=\frac{(4 + 9)\times6}{2}=\frac{13\times6}{2}=39\) \(mm^2\)

Step3: Calculate the area of the first rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the rectangle with \(l=(6 + 7+3)\) mm and \(w = 5\) mm. \(A_2=(6 + 7+3)\times5=16\times5 = 80\) \(mm^2\)

Step4: Calculate the area of the second rectangle

For the rectangle with \(l = 4\) mm and \(w=2\) mm. \(A_3=4\times2=8\) \(mm^2\)

Step5: Sum up the areas

\(A=A_1+A_2+A_3=39 + 80+8\)

Answer:

\(127\) \(mm^2\)