Question

Given a rectangular Parallelipiped with base a by b and altitude c. Find the area of the
section which contains two diagonally opposite edges of the parallelepiped.

Answer 1

Answer on Question #57585– Math – Geometry

Question

Given a rectangular Parallelepiped with base $a$ by $b$ and altitude $c$. Find the area of the section which contains two diagonally opposite edges of the parallelepiped.

Solution

We must find area of $AA_{1}C_{1}C$

Given $AA_{1}C_{1}C$ is a rectangle, so its area is

$$A_{AA_{1}C_{1}C} = AA_{1} \cdot AC$$

Given $\Delta ADC$ is a right triangle, so

$$AC = \sqrt{a^{2} + b^{2}}.$$

Thus, area of $A_{1}C_{1}C$ is equal to

$$A_{AA_{1}C_{1}C} = AA_{1} \cdot AC = c \sqrt{a^{2} + b^{2}}.$$

Answer: $c\sqrt{a^{2} + b^{2}}$

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