Question

A. Decompose this polygon so that its area can be calculated. All measurements are in centimeters.B. Calculate its area. Organize your work so that it can be followed by others.

Answer 1

70 cm²

1) Examining the figure we can decompose that polygon into

triangles

trapezoids

rectangle

2) So we can see that in here:

Now we can calculate the area

Trapezoids:

`S=((B+b)h)/(2)\text{ }\Rightarrow S=((6+2)2)/(2)\Rightarrow S=8`

There are 2 trapezoids so 16cm²

Rectangle:

S = w*l

S= 3 *12 = 36 cm²

Triangle:

S= 1/2(b*h)

S = 1/2(36)

S= 18 cm²

We have two triangles so =

3) So the answer is

16cm² + 18cm² + 36cm²=70cm²