Answer:
[tex]372cm^{2}[/tex]
Step-by-step explanation:
For this problem, let's find the surface area of each body and then add them.
1. Surface area of the rectangular prism (red color body):
Formula: [tex]SA=2(wl+hl+hw)[/tex]; where w is width, w is height, and l is length.
a) Annotate the values.
l= 12
h= 3
w= 4
b) Substitute in the formula and calculate.
[tex]SA=2((4)(12)+(3)(12)+(3)(4))=2(48+36+12)=192cm^{2}[/tex]
2. Surface area of the triangular prism (blue color body):
For this one we are gonna work part by part.
a) Let's calculate the area of the 2 triangular sides first.
Area of a triangle: [tex]A=\frac{b*h}{2}[/tex]; where b is base and h is height is the triangle.
[tex]A=2(\frac{(5)(12)}{2})=2(\frac{60}{2}) =60cm^{2}[/tex]
Note: we mltiply by 2 because there are 2 sides with this shape in the body.
b) Area of the back side that touches the rectangular prism.
This part is just a rectangle, hence, it's area formula is:
[tex]A=b*h=(12)(4)=48cm^{2}[/tex]
c. Area of the plane that forms a slope.
Is basically another rectangle, hence:
[tex]A=b*h=(13)(4)=52cm^{2}[/tex]
d. Area of the part next to the text "5 cm":
Is basically another rectangle, hence:
[tex]A=b*h=(4)(5)=20cm^{2}[/tex]
e. Now, the total surface area of this rectangular prism should be the addition of all it's partial areas:
[tex]60+48+52+20=180cm^{2}[/tex]
3. Surface area of the composite figure:
[tex]192cm^{2} +180cm^{2} =372cm^{2}[/tex]
