Which one of the following letters would be considered formal?

A regular hexagon is circumscribed about a circle with a radius of 6. Find the area of the shaded region shown. Give the exact a

Alecsey [184]

Answer:

19.58 unit²

Step-by-step explanation:

To find the area of the shaded region, we use the formula:

$A_{shaded}=A_{circle} - A_{hexagon}\\\\$

As we know that,

$A_{circle} = \pi r^2$ = $\pi 6^2$

=36πunit²

Next is to split up the hexagon into 6 regular triangles.

$A_{hexagon} = 6. A_{triangle}$

=6 x $\frac{1}{2} bh$

the base is equal to the radius i.e 6 as the triangles are regular.The height can be represented by taking one of the triangles and drawing a line down the middle.

So, the newly formed triangle is a 30°-60°90° right triangle.

(see figure 1 in attachment)

Here, a= 6/2=> 3

h= a√3 => 3√3

Substituting the required values in the formula of area of hexagon, we get

$A_{hexagon}= 6.\frac{1}{2}.6.3\sqrt{3}$ => 54√3unit²

$A_{shaded}=A_{circle} - A_{hexagon}\\\\$

=36π-54√3

= 19.58 unit²

4 0

3 years ago

The side of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeters units

yuradex [85]

(2,0) (5.0) (5,3) (2,3)
(2,0) (-1,0) (2,3) (-1,3)

3 0

3 years ago

Find rhe volume of a cylinder with a diameter of 10 inches and a height of 20 inches

IrinaK [193]

Since the diameter of the cylinder is 10, its radius is half that, or 5, thus

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=5\\
h=20
\end{cases}\implies V=\pi (5)^2(20)$

7 0

3 years ago

John is building a fence around his home currently his fence measures 14 feet on each side but he wants to increase only the wid

nalin [4]

Answer:

The dimensions of rectangular fence are 14 feet and 20 feet.

Step-by-step explanation:

We are given the following in the question:

Length of rectangular fence = 14 feet

Width of fence = (14+x) feet

Area of rectangular field = 280 square feet

Area of rectangular field =