Inference analysis: To infer the area formula of equilateral triangle, we must start with the area formula of ordinary triangle. From the base × height ÷2 of an ordinary triangle, the base × height ÷2 of an equilateral triangle is obtained, but the particularity of an equilateral triangle should be brought into play here. Three sides of an equilateral triangle are equal and all three angles are 60 degrees. The height from the bottom of an equilateral triangle can be composed of three lines of an isosceles triangle (an equilateral triangle is a special isosceles triangle). This height line is also the bisector and the median line. Let's look at the bisector, which divides a vertex of an equilateral triangle into two angles of 30, and at the same time plays the role of a high line, that is, an angle of 90. At this time, an equilateral triangle is divided into two right-angled triangles with an angle of 30. It should be noted that there is a right triangle with an angle of 30. This condition is very special, and it is a knowledge point that must be understood when doing geometric proof. It determines the length of three sides, and the ratio is 1:√3. : 2, 1 is a short right-angled side, √3. It is a long right-angled side, and 2 is a hypotenuse. The height of the equilateral triangle is √3. Half-bottom era.

Inference result: S equilateral△

= 1/2a×h

= 1/2a×√3.× 1/2×a

=√3.× 1/4a

=√3./4a

Function of formula: As long as you have this formula and know the bottom of an equilateral triangle, you can calculate its area.