Question

PLEASE HELP! WILL GIVE 70 POINTS!!

What is the surface area of the right triangular prism below?

Answer 1

`A=189\ mm^2`

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

`\displaystyle A_t=2*(b.h)/(2)=b.h=(4.5)(6)=27 mm^2`

The front area is a rectangle of dimensions 7.7 mm and 9 mm, thus

`A_f=b.h=(7.5)(9)=67.5 \ mm^2`

The back left area is another rectangle of 4.5 mm by 9 mm

`A_l=b.h=(4.5)(9)=40.5 \ mm^2`

Finally, the back right area is a rectangle of 6 mm by 9 mm

`A_r=b.h=(6)(9)=54 \ mm^2`

Thus, the total surface area of the prism is

`A=A_t+A_f+A_l+A_r=27+67.5+40.5+54=189\ mm^2`

`\boxed{A=189\ mm^2}`