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:

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

Try another example

Showing 0 comments:

Next similar math problems:

• Center traverse
  It is true that the middle traverse bisects the triangle?
• Rhombus
  PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.
• 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.
• Round table tablecloth
  Round table has area 50.24 dm². Calculate the diameter of the circular tablecloth, if it is extend beyond the edge of the table by 30 cm.
• Circle - simple
  Calculate the area of a circle in dm², if its circumference is 31.4 cm.
• Diameter to area
  Find the area of a circle whose diameter is 26cm.
• 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.
• Area of a triangle
  What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3?
• 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.
• Diameter
  What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
• Inscribed circle
  The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
• 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?
• CD disc
  A compact disc has a diameter of 11.8 cm. What is the surface area of the disc in square centimeters?
• Areaf of ST
  It is given square DBLK with side |BL|=13. Calculate area of triangle DKU if vertex U lie on line LB.
• 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?
• 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?
• Concentric circles
  There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?