Question

A slice is made perpendicular to the base of a right rectangular pyramid through the vertex. What is the area of the resulting two-dimensional cross section? Enter you answer in the box.

Answer 1

Area is a measure of space occupied in 2 dimensions. The area of the considered two dimensional cross section is:

• $\dfrac{1}{2}L.h \: \rm unit^2$ (if cross section is with respect to length)
• $\dfrac{1}{2}W.h \: \rm unit^2$ (if cross section is with respect to width)
• $\dfrac{1}{2}D.h \: \rm unit^2$ (if cross section is with respect to diagonal)

What is a cross section?

When some high dimensional object is sliced by hyperplane, then the area of the intersection of the hyperplane with the object is the cross-section.

For the given case, the right rectangular pyramid sliced will be having a triangle with height same as that of the pyramid but base equal to either length or the width of the base rectangle, or the diagonal.

Thus, if we consider: L = length of base, W = width of base , D = diagonal's length of the base of the rectangular pyramid, with the height h units, then we get the cross section's area as:

• $\dfrac{1}{2}L.h \: \rm unit^2$ (if cross section is with respect to length)
• $\dfrac{1}{2}W.h \: \rm unit^2$ (if cross section is with respect to width)
• $\dfrac{1}{2}D.h \: \rm unit^2$ (if cross section is with respect to diagonal)

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