Answer:
x= 2√37
Step-by-step explanation:
First thing you want to do is find the length of the missing side where the the right angle is at. You can find that with the pythagorean theorem of the other triangle, since you are already given 2 sides.
Pythagorean Theorem
a=2
b=?
c=2√2
Plug in and solve for b.
2^2+b^2=(2√2)^2
4+b^2=8
b^2=4
b=2
Now use the pythagorean theorem again to find your x side.
a=2
b=12
c=?
2^2+12^2=c^2
4+144=c^2
148=c^2
c=√148
c=2√37
The total area of pyramid is 113.569 square units
The equation to find the total area of the pyramid is Total area = base area + lateral area.
<u>Solution:</u>
Given, A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6.
<em><u>The total area of pyramid is given by:</u></em>
---- eqn 1
Where,
<em><u>The area of base is given as:</u></em>
Where "l" is the side of hexagon.
Substituting we get,
<em><u>The lateral area is given as:</u></em>
Where,
b: base of the triangle
h: height of the triangle
Substituting we get,
Plugging in the values we found in eqn 1 we get,
A = 113.569 square units
<em><u>Summarizing the results:</u></em>
The total area of pyramid is 113.569 square units approximately
The equation used to find total area of pyramid is Total area = base area + lateral area.
Volume of a cylinder is defined as:
v = volume
r = radius
h = height.
V = (r^2)h
In this problem,
v = 1,356.48 in^3
r = 6 in
h = ?
Plug our numbers into the volume formula above.
1,356.48 in^3 = (6^2)h
Divide both sides by (6^2) to isolate variable h
12.0 = h
The height of the cylinder is 12.0 inches