Atriangular prism has a volume of 2040 units. the dimensions of the base of the prism are shown below.
what is the height of the prism?
96 units
6.76 units
21.25 units
10.63 units

Height = 21.25 units

Step-by-step explanation:

Triangular prism (with triangular base at bottom) will have volume formula as:

Triangular Prism Volume = area of base * height

We need to find area of base (which is the triangle shown).

We can use heron's formula which is:

Where

A is area

p is HALF of the perimeter (sum of all sides)

a,b,c are the three sides

So p = (12+16+20)/2=24

Now,

Thus,

Volume = 96 * height

2040 = 96 * height

height = 2040/96 = 21.25 units

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

answer

point o.

step-by-step explanation: