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

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.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.