Answer:
84 [tex]sm^2[/tex]
Step-by-step explanation:
The surface of this figure consist of six faces:
two right triangles with legs = 4 and 3 sm;
one rectangle with sides 5 and 6 sm;
one rectangle with sides 3 and 6 sm;
one rectangle with sides 4 and 6 sm.
The surface area of whole figure is the sum of areas of this faces.
[tex]S_{\triangle} = \frac{4\cdot 3}{2} = 6 sm^2[/tex] -- triangle area
[tex]S_{5,6} = 5\cdot 6 = 30 sm^2[/tex] -- rectangle 5x6 area
[tex]S_{3,6} = 3\cdot 6 = 18 sm^2[/tex] -- rect. 3x6 area
[tex]S_{4,6} = 4\cdot 6 = 24 sm^2[/tex] -- rect. 4x6 area
[tex]S_{surf} = 2\cdot S_{\triangle} + S_{5,6} + S_{3,6} + S_{4,6} = 2\cdot 6 + 30 + 18 + 24 = 84 sm^2[/tex]
