Advice 1: How to find the area of a regular triangle

The right triangleω is called a triangle with three equal sides. It has the following properties: all sides of the right triangle are equal and all angles equal to 60 degrees. The right triangle is isosceles.
You will need
  • Knowledge of geometry.
Instruction
1
Let the given side of a right triangle with length a=7. Knowing this triangle can easily calculate its area. To do this, use the following formula: S = (3^(1/2)*a^2)/4. Substitute in this formula the value a=7 and obtain the following: S = (7*7*3^1/2)/4 = 49 * 1,7 / 4 = 20,82. Thus received that the area of an equilateral triangle with side a=7 is equal to S=20,82.
2
If given the radius of the inscribed triangle of a circle, the formula area using the radius will look like the following:
S = 3*3^(1/2)*r^2, where r is the radius of the inscribed circle. Let the radius of the inscribed circle r=4. Place it into the previously written formula and get the following expression: S = 3*1,7*4*4 = 81,6. That is, when the radius of the inscribed circle is 4 the area of an equilateral triangle will be equal to an 81.6.
3
When you know the radius of the circumscribed circle formula area of a triangle is: S = 3*3^(1/2)*R^2/4, where R is the radius of the circumscribed circle. Suppose that R=5, substitute this value into the formula: S = 3*1,7*25/4 = 31,9. It turns out that when the radius of the circumscribed circle is equal to 5 the area of a triangle is equal to 31.9.

Advice 2: How to find side of right triangle

"Correct" referred to the triangle whose sides are all of equal, and the angles at its vertices. In Euclidean geometry the angles at the vertices of such a triangle is not needed in the calculations - they are always equal to 60°, and the length of the sides can be calculated using relatively simple formulas.
Instruction
1
If you know the circle radius (r) inscribed in a right triangle, then find the lengths of its sides (a), increase the radius six times and divide the result by the square root of triples: a=r•6/√3. For example, if the radius is 15 centimeters, then the length of each side approximately equal to 15•6/√3≈90/1,73≈52,02 centimeters.
2
If you know the radius is not inscribed, and described next to such a triangle the circle (R), we assume that the radius of the circumscribed circle is always twice the inscribed radius. From this it follows that the formula for calculating the length of the sides (a) will almost be the same described in the previous step is known to increase the radius only three times, and the result divide by the square root of triples: a=R•3/√3. For example, if the radius of such a circle is 15 cm, the length of each side approximately equal to 15•3/√3≈45/1,73≈26,01 centimeters.
3
If we know the height (h) drawn from any vertex of the right triangle, to find the length of each side (a) find the quotient of twice the height on the square root of triples: a=h•2/√3. For example, if the altitude is 15 centimeters, then the lengths of the sides are equal 15•2/√3≈60/1,73≈34,68 cm.
4
If you know the length of the perimeter of the right triangle (P), for finding the lengths of the sides (a) of this geometric shape just reduce it three times: a=P/3. For example, if the perimeter is 150 cm, the length of each side is equal to 150/3=50 centimeters.
5
If you know only the area of the triangle (S), then find the length of each side (a) calculate the square root of the private from dividing the quadruple of the square on the square root of triples: a=√(4•S/√3). For example, if the area is 150 square centimeters, the length of each side approximately equal to √(4•150/√3)≈√(600/1,73)≈18,62 centimeters.
Note
The area of a triangle is always a positive value, as well as the length of a side of a triangle and the radii of the inscribed and circumscribed circles.
Useful advice
The radius of the inscribed and circumscribed circle in an equilateral triangle in two different times, knowing this, you can remember only one formula, for example, through the radius of the inscribed circle, and the second output, knowing this statement.
Search
Is the advice useful?