# 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 =  663.557 m2

#### Solution:

$a=10 \ \text{m} \ \\ r=15 \ \text{m} \ \\ \ \\ S_{1}=\sqrt{ 3 }/4 \cdot \ a^2=\sqrt{ 3 }/4 \cdot \ 10^2 \doteq 25 \ \sqrt{ 3 } \ \text{m}^2 \doteq 43.3013 \ \text{m}^2 \ \\ \ \\ S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 15^2 \doteq 706.8583 \ \text{m}^2 \ \\ \ \\ S=S_{2}-S_{1}=706.8583-43.3013=663.557 \ \text{m}^2$

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!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Areaf of ST
It is given square DBLK with side |BL|=13. Calculate area of triangle DKU if vertex U lie on line LB.
• Center traverse
It is true that the middle traverse bisects the triangle?
• Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
• 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?
• 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?
• 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.
• 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?
• 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?
• Wiring
Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
• 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
• 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.
• 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.
• Rhombus
PQRS is a rhombus. Given that PQ=3 cm & height of rhombus is given 2 cm. Calculate its area.
• CD disc
A compact disc has a diameter of 11.8 cm. What is the surface area of the disc in square centimeters?
• Diameter to area
Find the area of a circle whose diameter is 26cm.
• Circle - simple
Calculate the area of a circle in dm2, if its circumference is 31.4 cm.
• 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.