How to find radius of pentagon with apothegm?

The radius of a regular pentagon is the length of the line segment from any vertex to the opposite vertex diagonally opposite it. It can be easily found using Pythagorean Theorem. Using the length of the diagonal of the pentagon, the length of a side of the pentagon can be easily obtained by multiplying it with the square root of the remaining two sides, thus giving the radius.

How to find maximum area of isosceles triangle with apothegm?

You can use the Pythagorean theorem to find the length of the base of an isosceles triangle. Once you know that, you can find the area using the area of a triangle equation.

How to find volume of

Using the Heronian tetrakis to find the area of a pentagram is much simpler. The Heronian tetrakis is a tetrahedron whose four faces each have the same area as the base of a regular tetrahedron. Thus, the sum of the areas of the faces is equal to the area of a regular tetrahedron whose base has the same area as the base of the original tetrakis. The volume of the Heronian tetrakis is therefore equal

How to find radius of isosceles triangle with apothegm?

An isosceles triangle has two sides with the same length. The angle between the two equal sides is also known as “base angle”. Now, if we are asked to find the radius of an isosceles triangle, it’s easy! Using Pythagoras’ Theorem, the radius of an isosceles triangle is:

How to find radius of isosceles triangle with area?

Given an isosceles triangle, the hypotenuse is the base of the triangle and length of each leg is equal. With an isosceles triangle, the radius of the base is equal to the radius of the sides. The area of an isosceles triangle is equal to 0.5 base * height.