6 regular polygon

It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm² (square centimeters) has a circle in which is inscribed the 6-gon.

Result

S =  64.952 cm²
S₂ =  13.588 cm²

Solution:

$a=5 \ \text{cm} \ \\ \ \\ S=\dfrac{ 3 }{ 2 } \cdot \ \sqrt{ 3 } \cdot \ a^2=\dfrac{ 3 }{ 2 } \cdot \ \sqrt{ 3 } \cdot \ 5^2 \doteq 64.9519 \doteq 64.952 \ \text{cm}^2$

$r=a=5 \ \text{cm} \ \\ \ \\ S_{2}=\pi \cdot \ r^2-S=3.1416 \cdot \ 5^2-64.9519 \doteq 13.5878 \doteq 13.588 \ \text{cm}^2$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. 6-gon
   Perimeter of regular hexagon is 113. Calculate its circumradius (radius of circumscribed circle).
2. Trio 2
   Decide whether trio of numbers is the side of a right triangle: 26,24,10.
3. Hypotenuse
   Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
4. Sidewalk
   The city park is a circular bed of flowers with a diameter of 8 meters, around it the whole length is 1 meter wide sidewalk . What is the sidewalk area?
5. Cable
   Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
6. RT 10
   Area of right triangle is 84 cm² and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
7. Pipe cross section
   The pipe has an outside diameter 1100 mm and the pipe wall is 100 mm thick. Calculate the cross section of this pipe.
8. Right triangle ABC
   Calculate the perimeter and area of a right triangle ABC, if you know the length of legs 4 cm 5.5 cm and 6.8 cm is hypotenuse.
9. Four ropes
   TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
10. Chord circle
    The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
11. Bridge
    The bridge arc has a span 34 m and height 3 m. Calculate the radius of the circle arc of this bridge.
12. Broken tree
    The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
13. CD disc
    A compact disc has a diameter of 11.8 cm. What is the surface area of the disc in square centimeters?
14. Lawns
    Before a sports hall are two equally large rectangular lawns, each measuring 40 m and 12 m. Maintenance of 10m² lawn cost 45 CZK yearly. On each lawn is circular flowerbed with a diameter 8 meters. How much money is needed each year to take on lawn care?
15. Common chord
    Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?
16. Broken tree
    The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
17. Windbreak
    A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?