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Heron's Formula

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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 obtuse-angle triangle and an acute-angle 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?

Return to
High School Triangles and Other Polygons
Index of Selected Answers to Common Questions

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