Understanding Triangle Properties and Calculations

The video tutorial explains how to find the area of triangle ABC using its perimeter and inradius. It introduces the concepts of perimeter and inradius, describes the incenter, and demonstrates how to calculate the area by dividing the triangle into smaller triangles. The tutorial derives the formula for the area as 1/2 times the inradius times the perimeter, and applies this formula to a right triangle example, showing how to find the inradius when given the area and perimeter.

What is the perimeter of a triangle?

• The area of the triangle

• The distance from the incenter to a vertex

• The sum of the lengths of all sides of the triangle

• The sum of the angles of the triangle

What is the inradius of a triangle?

• The sum of the triangle's angles

• The length of the longest side

• The distance from the incenter to a side of the triangle

• The radius of the circumscribed circle

Where is the incenter of a triangle located?

• At the orthocenter of the triangle

• At the centroid of the triangle

• At the intersection of the angle bisectors

• At the midpoint of the longest side

How can the area of a triangle be expressed using its inradius and perimeter?

• Area = inradius × perimeter × 2

• Area = 1/3 × inradius × perimeter

• Area = inradius × perimeter

• Area = 1/2 × inradius × perimeter

What is the semiperimeter of a triangle?

• The area divided by the inradius

• The perimeter divided by 2

• The perimeter divided by 3

• The sum of the angles divided by 2

In the formula for the area of a triangle using inradius and semiperimeter, what does 's' represent?

• The semiperimeter

• The side length

• The inradius

• The area

For a right triangle with sides 3, 4, and 5, what is the area?

• 6

• 10

• 12

• 15

What is the inradius of a right triangle with sides 3, 4, and 5?

• 0.5

• 3

• 2

• 1

If you know the inradius and perimeter of a triangle, what can you calculate?

• The length of the longest side

• The area of the triangle

• The height of the triangle

• The type of triangle

What is a key takeaway about the relationship between inradius, perimeter, and area?

• They are only useful for equilateral triangles

• They only apply to right triangles

• They are unrelated

• Knowing two allows you to find the third