How Many Shapes Can You Make with 4 Equilateral Triangles?

Understand the full background How Many Shapes Can You Make with 4 Equilateral Triangles with our in-depth report.

All three medians together divide a triangle into 6 equal parts, proof

1. AAEG=AAFG, that is, a pair of adjacent triangles are equal in area.
2. This makes areas of all six triangles with coincident vertices at G equal.

What is the name given to a set of four triangles?

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

What solid can be made with 4 triangles?

The eight convex deltahedra

How to find the sum of equilateral triangles?

An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle a circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on indefinitely. Find the sum of the areas of all the triangles.

What is the area of an equilateral triangle?

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3 a 2 / 4. The perimeter of an equilateral triangle is 3a.

What kind of triangle has all three sides equal?

There are mainly three types of triangles which are scalene triangles, equilateral triangles, and isosceles triangles. An equilateral triangle has all the three sides equal and all angles equal to 60°. All the angles in an equilateral triangle are congruent. An equilateral triangle is the one in which all three sides are equal.