Question

How do I calculate the total surface of this shape?

Answer 1

The surface area of this figure is made by 1 rectangle in the bigger base, 1 rectangle in the smaller base, 2 lateral rectangles and 2 trapezoids.

In order to calculate the total surface area, let's calculate each individual area and sum them.

So we have:

`\begin{gathered} \text{Bigger base:} \\ A_1=18\cdot6=108 \\ \text{smaller base:} \\ A_2=9\cdot6=54 \\ \text{lateral rectangles:} \\ A_3=15\cdot6=90 \\ A_4=12\cdot6=72 \\ \text{trapezoids:} \\ A_5=A_6=((18+9)\cdot12)/(2)=162 \end{gathered}`

Now, calculating the total area, we have:

`\begin{gathered} S=A_1+A_2+A_3+A_4+A_5+A_6 \\ S=108+54+90+72+162+162 \\ S=648\text{ cm}^2 \end{gathered}`

Therefore the total surface area is 648 cm².