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.