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 1

Hint:- We have to only draw a shape having eight sides because a regular octagon is a type of polygon having eight sides and the length of each side is equal.

Complete step-by-step answer:
As we know that any polygon is a closed shape that is plane and described by joining the finite number line segments to form a closed figure.
As the polygon is a closed figure. So, it must have a minimum of three sides.
And polygons can have all sides equal or not.
But a regular polygon always has all sides equal.
And the name of the polygon is given on the basis of the number of sides it has.
Like 3-sided polygon is triangle, 4-sided is quadrilateral, 5-sided is pentagon, 6-sided is hexagon, 7-sided is heptagon, 8-sided is octagon, 9-sided is nonagon and 10-sided is decagon.
So, as we are asked to draw a regular octagon. So, let us draw a polygon with 8 equal sides.
 

Now as all the sides of the octagon ABCDEFGH are equal. And as we know that two opposite sides of the rectangle are equal. So, AB = EF and AF = BE (regular octagon). So,
 ABEF will be the required rectangle. There can also be three other possible rectangles and that are BCFG, CDGH and DEHA.
Hence, the required sketch will be ABCDEFGH.

Note:- Whenever we come up with this type of problem then remember that if there was given in the question that the polygon is regular then we had to draw a polygon with all sides equal but if regular is not given then the sides can or cannot be equal. And square paper is the paper of our notebook or we can say that square paper is ruled paper or printed in squares.