Question

what is the area of this figure?

Explanation:

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a = 4\) mm, \(b=5\) mm, and \(h = 6\) mm.

$$A_1=\frac{(4 + 5)\times6}{2}=\frac{9\times6}{2}=27\space mm^2$$

Step2: Calculate the area of the large rectangle

The formula for the area of a rectangle is \(A = l\times w\). The length \(l=(9 - 4)=5\) mm and the width \(w=(2+7 + 3)=12\) mm.

$$A_2=5\times12 = 60\space mm^2$$

Step3: Calculate the area of the small rectangle

The formula for the area of a rectangle is \(A=l\times w\), where \(l = 2\) mm and \(w=4\) mm.

$$A_3=2\times4=8\space mm^2$$

Step4: Sum up the areas

$$A=A_1+A_2+A_3=27 + 60+8=95\space mm^2$$

Answer:

\(95\space mm^2\)