Question

Which expression represents the area of the base of the pyramid? startfraction 3 v over h endfraction units2 (3v – h) units2 (v – 3h) units2 startfraction v over 3 h endfraction units2

Answer 1

The expression that represents the area of the base of the pyramid(right pyramid) is given by: Option A: 3v/h unit²

What is a right rectangular pyramid?

A right rectangular pyramid is a pyramid, with four slant sides, and a rectagular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.

How to find the volume and base's area of a right rectangular pyramid?

Suppose the base of the pyramid has length = l units, and width = w units.

Suppose that the height of the pyramid is of h units, then:

$v = \dfrac{l \times w \times h}{3} \: \rm unit^3$ is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

$b = l \times w\: \rm unit^2$

Thus, we can express the area of its base in terms of its volume as:

$v = \dfrac{l \times w \times h}{3} \: \rm unit^3 = \dfrac{b\times h}{3}\\\\3v = b\times h\\\\\\b = \dfrac{3v}{h} \: \rm unit^2$

Thus, the expression that represents the area of the base of the pyramid (right pyramid) is given by: Option A: 3v/h unit²

Learn more about right rectangular prism here:

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