Surface Area of Prisms and Cubes

This lesson explores how congruent faces simplify finding the surface area of 3D solids. It begins by reviewing congruent faces in rectangular prisms and cubes, then defines surface area as the sum of the areas of all faces. The lesson outlines a plan to calculate surface area by identifying face sizes and edge lengths. Examples include prisms with varying face sizes and a cube with congruent square faces. The lesson concludes with a review of different surface area calculation methods.

What is the benefit of using congruent faces when calculating surface area?

• It simplifies the calculation process.

• It makes the calculation more complex.

• It has no effect on the calculation.

• It increases the number of calculations needed.

How is surface area defined in the context of 3D solids?

• The volume of the solid.

• The sum of the lengths of all edges.

• The difference between the largest and smallest face areas.

• The sum of the areas of all faces.

What are the two key questions to ask when planning to find the surface area of a prism?

• What is the volume and density of the prism?

• What is the color and texture of the prism?

• How many vertices and edges are there?

• How many different face sizes and edge lengths are there?

In a prism with three different face sizes, what is the plan to calculate the surface area?

• Add the areas of all faces without any multiplication.

• Use only the largest face area for the calculation.

• Calculate the volume first and then find the surface area.

• Multiply the area of each face by the number of similar faces and sum them.

How many edge lengths are there in a prism with two face sizes?

• Two

• One

• Four

• Three

What is the calculation plan for a prism with two face sizes and two edge lengths?

• Use the perimeter of the base to find the surface area.

• Multiply the area of the rectangle by four and the square by two, then sum them.

• Add the areas of all faces without any multiplication.

• Multiply the area of the larger face by six.

How many congruent square faces does a cube have?

• Eight

• Six

• Five

• Four

What is the straightforward plan for calculating the surface area of a cube?

• Multiply the area of one face by four.

• Multiply the area of one face by six.

• Use the volume to find the surface area.

• Add the areas of all faces without any multiplication.

Which type of prism has the most complex formula for surface area calculation?

• A sphere with no faces.

• A prism with three different face sizes.

• A cube with six congruent faces.

• A prism with two face sizes.

What is the key takeaway from the lesson on finding surface area using congruent faces?

• Surface area is unrelated to face congruence.

• Congruent faces complicate surface area calculations.

• Using congruent faces simplifies the process of finding surface area.

• Surface area can only be calculated for cubes.