Question & Answer
QUESTION

Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

ANSWER Verified Verified
Hint – Here we will proceed by constructing an octagon such that all sides of the octagon are equal. Then, we will join four vertices which is the property of a regular octagon. Hence we will get the desired result.

Complete step-by-step answer:

Regular octagon is a closed shape with sides of equal length and interior angles should be of the same measurement.
In the given question,
ABCDEFGH is the required octagon which is regular.
$ \Rightarrow $ This implies that all the sides of the octagon are equal.
So,
In this octagon, we can join A and D and H and E can be joined to make a rectangle inside the octagon.
Also A, D, H, E are the four vertices of the octagon.
But this is possible only in the case of the regular octagon.
Therefore, ADEH is the required rectangle inside the octagon ABCDEFGH.
Note – We must know the properties of rectangle and regular octagon as it is used in the above question to construct the required figure. Also we should understand the right vertices to join because many of us can get confused in it.