Volume and Area of Prisms and Triangles

The video tutorial explains how to calculate the volume of a triangular prism using different methods. It starts with a basic example using given dimensions, then moves on to a right triangle example using the Pythagorean theorem. The tutorial also covers an equilateral triangle example and concludes with a complex example using Heron's formula for a triangle with three given sides. Each example demonstrates the step-by-step process of finding the area of the base and multiplying it by the height of the prism to find the volume.

What is the formula for calculating the volume of a triangular prism?

• Base times height divided by two

• Length times width times height

• Base times height of the triangle

• Area of the base times height of the prism

In the first example, what is the area of the base of the triangular prism?

• 120 square centimeters

• 90 square centimeters

• 60 square centimeters

• 30 square centimeters

How do you find the height of a triangle using the Pythagorean theorem?

• Subtract the base from the hypotenuse

• Multiply the base and hypotenuse

• Add the base and hypotenuse

• Use the formula a^2 + b^2 = c^2

What is the volume of the triangular prism in the second example?

• 120 cubic inches

• 90 cubic inches

• 60 cubic inches

• 30 cubic inches

What is the formula for the area of an equilateral triangle?

• s^2

• s^2 * sqrt(2) / 4

• s^2 * sqrt(3) / 4

• s^2 / 2

In the third example, what is the volume of the prism with an equilateral triangle base?

• 192 cubic inches

• 192 times the square root of 3 cubic inches

• 332.8 cubic inches

• 192 times the square root of 2 cubic inches

What is Heron's formula used for?

• Calculating the volume of a prism

• Determining the height of a triangle

• Finding the area of a triangle with all sides known

• Calculating the perimeter of a triangle

In the final example, what is the semi-perimeter (s) of the triangle?

• 15

• 10

• 25

• 20

What is the area of the base in the final example using Heron's formula?

• 50 square root 2 square centimeters

• 30 square root 2 square centimeters

• 40 square root 2 square centimeters

• 60 square root 2 square centimeters

What is the approximate volume of the prism in the final example?

• 763.7 cubic centimeters

• 540 cubic centimeters

• 700 cubic centimeters

• 600 cubic centimeters