Understanding Heronian Triangles

The video explores Hero triangles, which have integer sides and area. It discusses their properties, including examples where perimeter equals area, and introduces Hero's formula for calculating triangle area without knowing the height. The video also covers unique triangle pairs with the same perimeter and area, and mentions recent discoveries in the field.

What is a Heronian triangle?

• A triangle with no right angles

• A triangle with integer sides and area

• A triangle with equal sides

• A triangle with an irrational area

Tags

CCSS.2.G.A.1

How many triangles have the same perimeter and area?

• Three

• Five

• Seven

• Ten

Tags

CCSS.2.G.A.1

What happens to the area when you double the perimeter of a triangle?

• It doubles

• It triples

• It remains the same

• It quadruples

Tags

CCSS.6.G.A.1

Which type of triangle cannot have an integer area?

• Isosceles

• Equilateral

• Scalene

• Right-angled

Tags

CCSS.6.G.A.1

What is Hero's formula used for?

• Calculating the perimeter of a triangle

• Finding the height of a triangle

• Calculating the area of a triangle without knowing the height

• Determining if a triangle is right-angled

What is the semi-perimeter in Hero's formula?

• Half of the area

• Half of the perimeter

• Twice the perimeter

• Twice the area

Tags

CCSS.2.G.A.1

How many triangles have an area double the perimeter?

• Eighteen

• Five

• Ten

• Twenty

Tags

CCSS.8.G.A.2

What is unique about the pair of triangles discovered in 2018?

• They are both equilateral

• They have the same perimeter and area but different types

• They are both right-angled

• They have irrational areas

Tags

CCSS.4.G.A.2

What is a near-equilateral triangle?

• A triangle with all sides equal

• A triangle with sides close to being equal

• A triangle with no equal sides

• A triangle with one side much longer

Tags

CCSS.3.MD.D.8

What is the perimeter of a triangle with sides 13, 14, and 15?

• 42

• 44

• 46

• 40

Tags

CCSS.3.MD.D.8