Answer:
[tex]A=189\ mm^2[/tex]
Step-by-step explanation:
Surface Areas
Is the sum of all the lateral areas of a given solid. We need to compute the total surface area of the given prism. It has 5 sides, two of them are equal (top and bottom areas) and the rest are rectangles.
Computing the top and bottom areas. They form a right triangle whose legs are 4.5 mm and 6 mm. The area of both triangles is
[tex]\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2[/tex]
The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus
[tex]A_f=b.h=(7.5)(9)=67.5 \ mm^2[/tex]
The back left area is another rectangle of 4.5 mm by 9 mm
[tex]A_l=b.h=(4.5)(9)=40.5 \ mm^2[/tex]
Finally, the back right area is a rectangle of 6 mm by 9 mm
[tex]A_r=b.h=(6)(9)=54 \ mm^2[/tex]
Thus, the total surface area of the prism is
[tex]A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2[/tex]
[tex]\boxed{A=189\ mm^2}[/tex]
