Surface Area of Square Pyramids

The video tutorial explains how to calculate the surface area of a square pyramid using the formula: surface area equals two times the base length times the slant height plus the base length squared. It demonstrates solving for whole number dimensions of the base and slant height when the surface area is 56 square inches. The tutorial explores different base lengths to find valid solutions and sketches the corresponding pyramid faces.

What is the formula for the surface area of a square pyramid?

• Surface area = b^2 + 4bs

• Surface area = 4b + S^2

• Surface area = 2b + 4S

• Surface area = 2bS + b^2

Why can't b be zero when solving the surface area equation?

• Because it would make the surface area zero

• Because it would make the equation unsolvable

• Because it would make the slant height zero

• Because it would make the base length infinite

What is the result of solving the equation with b = 1?

• s = 10, which is not a whole number

• s = 13, which is a whole number

• s = 27.55, which is not a whole number

• s = 5, which is a whole number

What are the values of b and s when a valid solution is found with b = 2?

• b = 2, s = 5

• b = 2, s = 13

• b = 2, s = 8

• b = 2, s = 10

What is the surface area of the pyramid when b = 2 and s = 13?

• 56 square inches

• 65 square inches

• 45 square inches

• 50 square inches

Why does b = 3 not provide a valid solution?

• Because s is not a whole number

• Because b and s are both zero

• Because the surface area exceeds 56

• Because the base length is too large

What is the second valid solution found for b and s?

• b = 3, s = 10

• b = 4, s = 5

• b = 5, s = 4

• b = 4, s = 10

What is the base length of the square pyramid when b = 4?

• 2 inches

• 3 inches

• 5 inches

• 4 inches

What is the slant height of the pyramid when b = 4?

• 13 inches

• 8 inches

• 10 inches

• 5 inches

What is the significance of finding whole number solutions for b and s?

• It allows for more solutions

• It makes the calculations easier

• It satisfies the given conditions of the problem

• It ensures the pyramid is symmetrical