Question

Which are true about the pyramid? Check all that apply.
The base of the pyramid is a square with four sides, each measuring 756 feet.
The slant height of the pyramid is 612 feet.
The slant height of the pyramid is 756 feet.
All four triangular faces are congruent.
All four triangular faces are not congruent.
The pyramid has four lateral faces.

Answer 1

The statements that are true about the pyramid are

• The base of the pyramid is a square with four sides, each measuring 756 feet.

• The slant height of the pyramid is 612 feet.

• All four triangular faces are congruent.

• The pyramid has four lateral faces.

Properties of a Square pyramid

From the question, we are to determine the statements that are true about the pyramid

The diagram shows a square pyramid,

The length of a side of its base is 756 ft

and

The height / altitude of a triangular face is 612 ft

Since the pyramid is a square pyramid,

Then, the base must be a square with each side measuring 756 feet

∴ The first statement is true

Since the height of a triangular face is 612 ft,

Then,

∴ The slant height of the pyramid is 612 feet

NOTE: Slant height of a pyramid is the altitude of the triangle comprising a lateral face

Thus, the second statement is true

Since the triangular faces each have a base of 756ft and a height of 612 ft,

Then,

All four triangular faces are congruent

∴ The fourth statement is true

NOTE: Lateral sides of a solid are the faces on the sides of the shape

The pyramid has four lateral faces which are each a triangle

∴ The last statement is true

Hence, the statements that are true about the pyramid are

• The base of the pyramid is a square with four sides, each measuring 756 feet.

• The slant height of the pyramid is 612 feet.

• All four triangular faces are congruent.

• The pyramid has four lateral faces.

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