1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Reika [66]
3 years ago
15

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid

has a regular hexagonal base with a radius of 2 x units and an apothem of x StartRoot 3 EndRoot units. Which expression represents the area of the base of the pyramid? x squared StartRoot 3 EndRoot units2 3 x squared StartRoot 3 EndRoot units2 4 x squared StartRoot 3 EndRoot units2 6 x squared StartRoot 3 EndRoot units2

Mathematics
2 answers:
Xelga [282]3 years ago
5 0

Answer:

6 x^2*\sqrt{3}

Step-by-step explanation:

The base of the pyramid we need to study is a hexagon.

Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.

Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")

Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.

We know the area of a triangle is the product of its base times its height, divided by 2: \frac{base*height}{2} = \frac{2x*height}{2}

We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures x\sqrt{3}, so replacing this value in the formula above for the area of one of the triangles:

\frac{2x*height}{2}= \frac{2x*x\sqrt{3} }{2}=x^2\sqrt{3}

Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):

Area of hexagon = 6x^2\sqrt{3}

which is the last option given in the list.

RUDIKE [14]3 years ago
3 0

Answer:

D

Step-by-step explanation:

You might be interested in
The Sanchez family is going on a vacation. If they drive for 3 hours at 65 mph, how many miles will they travel?
wariber [46]
v-speed\\s-distance\\t-time\\\\v=\frac{s}{t}\to s=vt\\\\v=65\ mph;\ t=3h\\\\s=65mph\times3h=195mi\\\\Answer:195miles.

3 0
3 years ago
Read 2 more answers
Simplify. 9x^8-18x^6
GrogVix [38]
You cannot simplify this but you can factorise it:

9x^6 (x^2 - 2)
7 0
3 years ago
What is 10 less than 14 in algebraic expression?
Cerrena [4.2K]

14-10=? less than indicates that a minus sign is needed.

7 0
3 years ago
Use the Angle Addition Postulate to find the measure of the unknown angle
Artyom0805 [142]

Answer:

Hey there!

Step-by-step explanation:

This is ur answer....

<h2><em>61 + 42 = 103</em></h2>

<h2><em>ABC </em><em>=</em><em> </em><em>1</em><em>0</em><em>3</em></h2>

Hope it helps!

Brainliest pls!

Follow me!

3 0
1 year ago
Tell me both like what should i say in the sentence please ​
Black_prince [1.1K]
1 is yes and 2 is no epa
4 0
3 years ago
Other questions:
  • A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength
    15·1 answer
  • State whether f is a function
    6·2 answers
  • 48oz sprite for $1.39 or 32 oz dr. pepper for $0.89?
    13·1 answer
  • Another company offers a rate os $0.05 per minute. How would you find the unit rate per hour
    6·2 answers
  • I need help urgently!!!
    11·1 answer
  • What is a positive coterminal angle to 403° that is between 500° and 1000° and a negative coterminal angle to 403° that is betwe
    10·2 answers
  • sherane rolls a standard, six-sided number cube. what is the probability of rolling a multiple of 3?​
    12·2 answers
  • 9/12 - 1/3 ? help i will mark brainly
    7·2 answers
  • department store sells a pair of shoes with a 33% discount coupon. If the store orignially sold the shoes for $55.25, what is th
    9·1 answer
  • Can someone explain this to me like do I do division so get the answer or?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!