if someone could answer at least one for me that would be awesome! TYYY :D

Answer:

1. 672 inches

Step-by-step explanation:

Question #1

The formula for the volume of a triangular prism is:

V = [tex]\frac{bh}{2}[/tex]

Where V is the volume, b is the area of the base, and h is the height. You are given the volume and the height. Plug those numbers into your equation.

[tex]4704 = \frac{b(14)}{2}[/tex]

Now, solve for b. To do this, you must isolate the variable b.

The first step to do this is to multiply both sides by 2. This will get you:

4704(2) = 14b

9408 = 14b

Now, divide both sides by 14 to get:

672 = b.

Therefore, the area of the base is 672 inches.

Question #2

To solve this problem, separate the figure into 2 shapes. You have a triangle with a base of 6 cm and a height of 6 cm, as well as a semicircle with a radius of 3 cm.

After you do this, find the area of each shape separately.

The formula for the area of a triangle is:

[tex]A = \frac{bh}{2}[/tex],

where A is the area, b is the length of the base, and h is the height. You know the base and the height, so plug those into your equation. You will get:

[tex]A = \frac{6*6}{2}\\\\A = \frac{36}{2}\\\\A = 18[/tex]

Now you know that the area of the triangle is 18 cm^2.

Let's find the area of the semicircle.

The formula for the area of a semicircle is:

A = [tex]\frac{1}{2}[/tex]π[tex]r^2[/tex]

You know the radius, so plug that in to get:

A = [tex]\frac{1}{2}[/tex]π([tex]3^2[/tex])

A = [tex]\frac{1}{2}[/tex]π(9)

Simplify this to get:

A = 4.5π.

Now, either multiply 4.5 by π to get:

14.1371669412 cm^2

or, multiply 4.5 by 3.14 to get:

14.13 cm^2.

Then, add the area of the triangle, 18 cm^2, by the area of the triangle, 14.13, to get:

32.13 cm^2.

Hope this helps!

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