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, \(b=9\) mm, and \(h = 6\) mm.

$$A_1=\frac{(4 + 9)\times6}{2}=\frac{13\times6}{2}=39\ \text{mm}^2$$

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the rectangle with \(l = 9\) mm and \(w=2\) mm, \(A_2=9\times2 = 18\ \text{mm}^2\). For the rectangle with \(l=(7 + 3)\) mm and \(w = 5\) mm, \(A_3=(7 + 3)\times5=50\ \text{mm}^2\)

Step3: Sum up the areas

$$A=A_1+A_2+A_3=39+18 + 50=107\ \text{mm}^2$$

Answer:

\(107\ \text{mm}^2\)