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
Goshia [24]
3 years ago
11

The base of a regular pyramid is a hexagon. The figure shows a regular hexagon with center C. An apothem is shown as a dashed se

gment perpendicular to an edge and is labeled as a. A dashed line segment joins the center with the left vertex of the edge perpendicular to the apothem. This segment has a length of 14 centimeters. The angle formed by the edge and the segment measures 60 degrees. What is the area of the base of the pyramid? Enter your answer in the box. Express your answer in radical form.
Mathematics
1 answer:
tatuchka [14]3 years ago
8 0
Answer: 294√3

Explanation:


1) The described hexagon has these featrues:
a) 6 congruent equilateral triangles whose side lengths measure 14
b) height of each triangle = apotema = a
c) the area of each triangle is base × a / 2 = 14 × a / 2 = 7a


2) a is one leg of a right triangle whose other leg is 14 / 2 = 7, and the hypotenuse is 14.

3) Then you can use Pythagorean theorem fo find a:

14² = 7² + a² ⇒ a² = 14² - 7² = 147 ⇒ a = √ 147 = 7√3

4) Therefore, the area of one triangle is: 14 × 7√3  / 2 = 49√3

5) And the area of the hexagon is 6 times that: 6 × 49√3 = 294√3
You might be interested in
Pythagorean theorem)
JulsSmile [24]

Answer: its b ;p

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9
Marizza181 [45]
The Answer is B = 7 > h > 9...
6 0
3 years ago
Read 2 more answers
Can someone help please!!
d1i1m1o1n [39]

Answer:

75.39 in^2 (round to the nearest hundreds)

Step-by-step explanation:

I think that we have to find the lateral area

circumference = 2 x radius x pi = 2 x 4 x pi = 25,13 in^2 (round to the nearest hundreds)

lateral surface = (circumference x slant height)/2 = (25,13 x 6)/2 = 75,39 in^2 (round to the nearest hundreds)

3 0
3 years ago
Johnny has 200 cupcakes he gave 10 to You and 20 to Your Teacher how many cupcake you gave away
Ilya [14]

Answer:

30 cupcakes

Step-by-step explanation:

10+20 equal 30

4 0
3 years ago
Read 2 more answers
Graph each inequality and graph its solution.<br> 3) n - 11 &gt; -21
Vera_Pavlovna [14]
The correct answer is
Inequality: n>-10
Interval Notation: (-10,infinity)
7 0
3 years ago
Other questions:
  • Ellen boughy a tray of plants for $8.15 there where 16 plants in the tray if i bought only one what would it cost
    5·2 answers
  • Three friends agree to save money for a graduation road trip. They decide that each of them will put 50.25 in the fund on the fi
    8·2 answers
  • A delivery truck traveled 133 miles in 3.5 hours. What was the average speed of the delivery truck in miles per hour
    5·2 answers
  • If y =18 and x=60 what is the constant of proportionality
    6·1 answer
  • A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard
    15·1 answer
  • Factor completely 4p^2-25q^2
    9·1 answer
  • F(x)= x^2 . What is g(x)?
    15·1 answer
  • Is y^4 x equal to xy^4?​
    7·1 answer
  • Vector u has initial point at (3, 9) and terminal point at (–7, 5). Vector v has initial point at (1, –4) and terminal point at
    8·2 answers
  • Avery got on the bus at 5:15 P.M. The trip took 80 minutes. Then she walked for 53 minutes to get home. At what time did Avery a
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!