Question

A pyramid is cut by a plane parallel to its base at a distance from the base equal to two-thirds the length of the altitude. The area of the base is $18$. Find the area of the section determined by the pyramid and the cutting plane.

• A. 1
• B. 2
• C. 3
• D. 6
• E. 9

Answer 1

Answer: (B)

2

Let the height of altitude be $h$, then the height of cutting base from vertex be $h/3$
Area of base is $18$, therefore the length of side will be $3\sqrt{2}$.
Let the length of cutting base be $l$
By similarity , we get $\frac{h/3}{h}=\frac{l}{3\sqrt{2}}$ $\Rightarrow l=\sqrt{2}$
Therefore the area of cutting base is $\sqrt{2}\times \sqrt{2}=2$.