What is interior point of equilateral triangle?

Let us consider an equilateral triangle ABC, I be interior point such that ID, IE, IF are perpendicular to sides BC, AC, AB respectively. ID + IE + IF = s. Now, area of equilateral triangle ABC = Area of triangle AIC + Area of triangle AIB + Area of triangle BIC. √3/4 × a2 = 1/2 × a × IE + 1/2 × a × IF + 1/2 × a × ID.

Which polygon contains equilateral triangle?

1 Answer. Equilateral triangle is a regular three-sided polygon. It has three interior angles of 60o each and three sides, equal in length. It’s an example of a convex polygon.

What is Viviani Theorem?

Viviani’s Theorem, discovered over 300 years ago, states that inside an equilateral triangle, the sum of the perpendicular distances from a point P to the three sides is in- dependent of the position of P (and so equals the altitude of the triangle).

Which of the polygon is an equilateral polygon?

A polygon with all sides equal is equilateral. One with all interior angles equal is equiangular. Any polygon that is both equilateral and equiangular is a regular polygon (e.g., an equilateral triangle or a square).

What is the formula of altitude of an equilateral triangle?

Altitudes of a Triangles Formulas

Triangle Type Altitude Formula
Equilateral Triangle h = (½) × √3 × s
Isosceles Triangle h =√(a2−b2⁄2)
Right Triangle h =√(xy)

Which point of concurrency is determined by the three altitudes of any triangle?

the orthocenter
The three altitudes of a triangle are concurrent. The point of concurrency is called the orthocenter.

What do you call an angle inside a polygon?

An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.

What do you call a polygon that is both equilateral and equiangular?

Regular Polygons When a polygon is both equilateral and equiangular, it is called a regular polygon. A square is an example of a regular polygon.

How do you prove Viviani’s Theorem?

This proof depends on the readily-proved proposition that the area of a triangle is half its base times its height—that is, half the product of one side with the altitude from that side. Let ABC be an equilateral triangle whose height is h and whose side is a.

What do you call the polygon which is both equilateral and equal?

When a polygon is both equilateral and equiangular, it is called a regular polygon. A square is an example of a regular polygon.

What do you call a polygon which is both equilateral and equiangular?

Regular polygons. When a polygon is both equilateral and equiangular, it is referred to as a regular polygon.