5.4.6 Exercises

	Calculate the area of the polygon to the right.

The values of the indicated subareas are calculated separately.

$F_{1}$ is a triangle: $F_{1} = \frac{15 \cdot 22}{2} = 165$ .
$F_{2}$ is a trapezoid that can be divided into two triangles with the altitude $25$ : $F_{2} = \frac{22 \cdot 25}{2} + \frac{26 \cdot 25}{2} = 275 + 325 = 600$ .
$F_{3}$ is a triangle: $F_{3} = \frac{14 \cdot 26}{2} = 182$ .
The surface $F_{4}$ is also a triangle: $F_{4} = \frac{(15 + 25 + 14) \cdot 18}{2} = 486$ .

Finally, we obtain the area of the entire polygon by summing up all these subareas:

F_{1} + F_{2} + F_{3} + F_{4} = 165 + 600 + 182 + 486 = 1433