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!
