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?

Correct result:

S =  663.5571 m²

Solution:

$$\begin{gathered} a=10\text{ m } \\ r=15\text{ m } \\ {S}_1=\sqrt{3}\mathrm{/}4\cdot a^2=\sqrt{3}\mathrm{/}4\cdot 10^2=25\sqrt{3}{\text{m}}^2\doteq 43.3013{\text{m}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 15^2\doteq 706.8583{\text{m}}^2 \\ r>a \\ S=S_2-S_1=706.8583-43.3013=663.5571{\text{m}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• 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
• Goat
  Meadow is a circle with radius r = 19 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
• An angle
  An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
• Parcel
  parcel has a rectangular shape of a trapezoid with bases 12 m and 10 m and a height 8 m. On parcel was built object with a footprint an isosceles triangle shape with side 4 m and height three-quarters of a meter. What is the area of unbuild parcel?
• 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?
• Seagull
  Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (w
• Roof tiles
  The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m² should be used 8 tiles?
• Water level
  How high is the water in the swimming pool with dimensions of 37m in length and 15m in width, if an inlet valve is opened for 10 hours flowing 12 liters of water per second?
• Triangular prism
  Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.
• 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.
• Quadrant II
  Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
• Pentadecagon
  Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Dog
  The dog is tied to a chain, which is mounted in the corner of the yard. Yard has the shape of a square with a side length of 20 meters. The same length is also a dog chain. Are there places in the yard where the dog can't reach?
• Rectangle area
  The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
• Concrete pedestal
  The carpenters made wooden mold on a concrete pedestal in the shape of a cube with edge 2 meter long. What is the area in which the concrete touches wooden molds? (No lid or bottom)
• Circle section
  Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont