# Equilateral triangle v3

Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle.

Result

S =  2.58 cm2

#### Solution:

$a=8 \ \text{cm} \ \\ r=a/2=8/2=4 \ \text{cm} \ \\ A=\dfrac{ 60 }{ 360 }=\dfrac{ 1 }{ 6 } \doteq 0.1667 \ \\ S_{1}=\sqrt{ 3 }/4 \cdot \ a^2=\sqrt{ 3 }/4 \cdot \ 8^2 \doteq 16 \ \sqrt{ 3 } \ \text{cm}^2 \doteq 27.7128 \ \text{cm}^2 \ \\ S_{2}=\pi \cdot \ r^2 \cdot \ A=3.1416 \cdot \ 4^2 \cdot \ 0.1667 \doteq 8.3776 \ \text{cm}^2 \ \\ \ \\ S=S_{1}-3 \cdot \ S_{2}=27.7128-3 \cdot \ 8.3776 \doteq 2.5801 \doteq 2.58 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. An equilateral
An equilateral triangle with a side 10 m represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?
2. Chord 2
Point A has distance 13 cm from the center of the circle with radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle.
3. Pendulum
Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
4. Center traverse
It is true that the middle traverse bisects the triangle?
5. Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
6. Ruler and compass
Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
7. Find the 9
Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
8. Field with vegetables
Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
9. Circles
Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
10. Chord
Point on the circle is the end point of diameter and end point of chord length of radius. What angle between chord and diameter?
11. Inscribed triangle
To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
12. Circular lawn
Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to 1
13. Ace
The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
14. Circle sector
Circular sector with a central angle 80 ° has area 1257 cm2. Calculate its radius r.
15. Disc
Circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc?
16. Slope
Find the slope of the line: x=t and y=1+t.
17. Regular octagon
Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.