Answer:
The surface area of the composite figure is [tex]410\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the surface area of the rectangular prism of the bottom plus the lateral area o the rectangular prism of the top
so
Step 1
Find the surface area of the rectangular prism of the bottom
The surface area is equal to
[tex]SA=2B+Ph[/tex]
Find the area of the base B
[tex]B=10*10=100\ m^{2}[/tex]
[tex]P=4*10=40\ m[/tex]
[tex]h=3\ m[/tex]
substitute
[tex]SA=2(100)+40(3)=320\ m^{2}[/tex]
Step 2
Find the lateral area of the rectangular prism of the top
The lateral area is equal to
[tex]LA=Ph[/tex]
[tex]P=2*(4+5)=18\ m[/tex]
[tex]h=5\ m[/tex]
substitute
[tex]LA=18(5)=90\ m^{2}[/tex]
Step 3
Find the surface area of the composite figure
[tex]320\ m^{2}+90\ m^{2}=410\ m^{2}[/tex]
