 Heron's Formula,
a selection of answers from the Dr. Math archives.
 Who was Hero (or Heron)?
 I have been trying to find information on the Greek mathematician
Hero.
 Heron's Formula
 How can I find the area of an isosceles triangle, an equilateral
triangle, a scalene triangle, an obtuseangle triangle and an acuteangle
triangle without the height being given?
 Proofs
 Proof of Hero's formula
 Could you tell me where to find a proof of Hero's formula or help
on how to derive it?
 Geometric Proof of Heron's Formula
 How can I prove Hero(n)'s formula using a circle with center P and
radius R inscribed in triangle ABC?
 Incircles Tangent to a Common Line
 In triangle ABC, the incircle touches side AB at M. T is an arbitrary
point on BC. How can I show that the incircles of triangles BMT, AMT and ATC
are all tangent to a common line?
 Proof of Heron's Area Formula
 I need to write a proof of Heron's Area Formula.
 Derivations of Heron's Formula
 How is Heron's formula (Hero's formula) derived?
 Using Heron's Formula
 Triangle Altitude and Area
 Using Heron's formula to find the altitude of a triangle whose
dimensions are given.
 Find the Smallest Triangle
 A triangle has sides whose lengths are consecutive integers. Its area
is a multiple of 20. Find the smallest triangle that satisfies these
conditions.
 The Area of Triangles using Hero's
Formula
 If a person gave three dimensions of a triangle (in feet) and noted the
base dimension, without knowing the angles because the other two lines would
have to intersect someplace, is there a formula that could calculate the area?
 Area of a Lawn
 I have two areas of lawn that I want to sod with new grass and
don't know how much sod to buy.
 Area of Inscribed Circle
 Find the area of the circle inscribed in a triangle ABC using
Heron's Law.
 Area of Triangles When Altitudes
Are Given
 Find the area of a triangle when the lengths of the three altitudes
are given.
 Congruent Triangles
 If two triangles have the same area and the same perimeter,
must they be congruent?
 Heron's Formula, Cartesian
Coordinate Plane
 If a triangle has sides 5, 6, and the square root of thirteen,
what is the area of the triangle?
 Distance to an Object
 Is there an easy way to measure the distance from a baseline to an
object if one knows the measurement of the baseline and both angles
leading toward the object?
 Square with same Perimeter and
Area as a Triangle
 I've been hunting for a square/triangle combination with the same
perimeter and area. Is this possible?
