Understanding Diagonals in Rectangular Prisms

The video tutorial explains how to calculate the diagonal length in cubes and rectangular prisms. It begins by introducing the concept and the need to apply the Pythagorean theorem twice. The tutorial then provides a detailed example using two triangles to find the diagonal of a rectangular prism with given dimensions. Finally, it demonstrates how to use a formula to achieve the same result more efficiently.

What is the first step in calculating the diagonal of a rectangular prism?

• Use a formula directly

• Apply the Pythagorean theorem once

• Measure the diagonal directly

• Create a right triangle with length and width

Tags

CCSS.8.G.B.8

Why do we need to apply the Pythagorean theorem twice when finding the diagonal of a rectangular prism?

• To ensure accuracy

• To account for the height of the prism

• To calculate the volume of the prism

• To find the area of the prism

Tags

CCSS.8.G.B.8

What is the length of the hypotenuse in the first right triangle formed in the rectangular prism example?

• 6 cm

• 8 cm

• 7 cm

• 10 cm

Tags

CCSS.7.G.B.6

After finding the hypotenuse of the first triangle, what is the next step?

• Find the surface area of the prism

• Calculate the volume of the prism

• Measure the diagonal directly

• Use the hypotenuse to form a second right triangle

What is the final length of the diagonal in the rectangular prism example?

• 10 cm

• 12.2 cm

• 14 cm

• 15.5 cm

Tags

CCSS.7.G.B.6

What is the advantage of using a formula to find the diagonal of a rectangular prism?

• It is more accurate

• It is faster and requires fewer steps

• It provides a different result

• It is easier to remember

Tags

CCSS.7.G.B.6

Which of the following is part of the formula for finding the diagonal of a rectangular prism?

• Length squared plus width squared plus height squared

• Length squared plus width squared

• Length plus width plus height

• Length times width times height

Tags

CCSS.8.G.B.8

What is the result of the formula for the diagonal in the example given?

• 10 cm

• 12.2 cm

• 14 cm

• 15.5 cm

Tags

CCSS.7.G.B.6

When is it appropriate to use the formula for finding the diagonal?

• When the dimensions are unknown

• When the prism is irregular

• When looking for the diagonal through the middle

• When the prism is a cube

What is the key takeaway from using the formula for finding diagonals?

• It is only for advanced learners

• It requires more calculations

• It is less accurate

• It simplifies the process