Question

Two prisms have equal heights and equal volumes. the base of one is a pentagon and the base of the other is a square. if the area of the pentagonal base is 36 square inches, how many inches are in the length of each side of the square base?

Answer 1

The length of the square base is 6 inches.

Answer 2

Length of each side of the square base of a prism is equals to 6inches.

What is volume?

"Volume is the total amount of space occupied by any three dimensional object enclosed in it."

Formula used

Volume of the Prism = Area of the base × height

Area of square = (side length)²

According to the question,

'V₁' represents volume of prism with pentagon base

'h₁'   represents height of prism with pentagon base

'A₁'  represents area of prism with pentagon base

'V₂'  represents volume of prism with square base

'h₂' represents height of prism with square base

'A₂' represents area of prism with square base

As per the condition given we have,

  h₁ = h₂

  V₁ =V₂

⇒A₁ h₁ = A₂ h₂

⇒  A₁ = A₂

Area of the pentagonal base 'A₁' = 36square inches

Therefore,

A₂ = 36

Substitute the value in the formula we get,

 (side length)² = 36

⇒ side length = √36

                       = 6inches

Hence, length of each side of the square base of a prism is equals to 6inches.

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