2 years ago

Need the answer to this question

Mathematics

1 answer:

Ipatiy [6.2K]2 years ago

3 0

Answer:

3 Rd one I think, it's correct

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PLEASE HELP! WILL GIVE 70 POINTS!!

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Answer:

$A=189\ mm^2$

Step-by-step explanation:

<u>Surface Areas </u>

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

$\displaystyle A_t=2*\frac{b.h}{2}=b.h=(4.5)(6)=27 mm^2$

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

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

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

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