The base of a right prism is a rhombus whose diagonals are 6 in and 8. if the altitude of the prism is 12, what is the total surface area of the prism?

The total surface area of the prism is

Step-by-step explanation:

we know that

The two diagonals of a rhombus are perpendicular and bisect each other

All sides are congruent

The surface area of a prism is equal to

where

B is the area of the base of prism

P is the perimeter of the base of prism

h is the height of the prism

step 1

Find the length side of the rhombus

Applying Pythagoras Theorem

we have

c is the length side of the rhombus

a and b are the semi diagonals of the rhombus

substitute

step 2

Find the perimeter of the base P

The perimeter of the rhombus is equal to

step 3

Find the area of the base B

The area of the rhombus is

D1 and D2 are the diagonals of the rhombus

substitute

step 3

Find the surface area of the prism

substitute the values

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

r = 78539458390583095803458309458039485093485 or just 3

step-by-step explanation: