With these instructions you will construct a regular octagon … Example. 4.) The perimeter of the square is 108 centimeters. The octagon, specifically the regular octagon, is made up of four sets of parallel sides with congruent interior and exterior angles. One of the sides of the octagon is meters.… So you want the area of seven of the squares, each of which is 9 cm by 9 cm. An illustration showing how to construct a regular octagon from a square by cutting off the corners… Octagon Circumscribed About a Square. An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. . However, if you want a regular octagon, the lengths must be around the ratio 7:10:7. Divide the lengths into thirds. Those points are the remaining vertices of an octagon. 3.) MCQ in Plane Geometry. Then, draw 2 diagonal lines that intersect at the center of the circle and split it up into 8 equal parts. With centre at B, take radius BO and draw the arc GJ. As shown above every side of regular octagon = X DC = DP + PQ + QC, Here, PQ = X & DP = QC = Y Now, we form the equations : What is the number of square centimeters in the area of the octagon? 2.) Then, fold the corners inwards so that the folds are the same length as the top, bottom, and sides of the paper. How to draw a regular octagon inside a given square. cm . Ask Question. Finally, erase the circle and the lines inside of the octagon. Inscribing an octagon 4. Draw a square, which is used to draw this octagon. If the circle center point is not given, you can construct the center using the method shown in Finding the center of a circle. The normal square was inscribed by connecting the diagonal diameters of the circle. Since a radius is given a ruler would be needed to set the compass at 3cm to draw the initial circle. You now have a square DFEG. Bisect each right angle external to the segment. This uses the property that the external angles of a regular octagan are each 45 degrees. Erase the unneeded sides such that it forms an octagon. Join the diagonals AC and BD to intersect at O; With centre at A, take radius AO and draw the arc EH. In fact every regular polygon has a circumcircle, and so can be inscribed in that circle. Draw nine radii separating the central angles. Online Questions and Answers in Plane Geometry. cm) of a regular octagon inscribed in a circle of radius 10 cm? For the triangles: the short sides are each 1/3 of the sides of the square: 9 cm. Construct four circles. From this you can calculate the area of the whole square. Connecting these points will make up your octagon. Construction. Construct a regular nonagon using the circle method: Draw a circle, and with a protractor place nine central angles of 40° each around the center (9 x 40° = 360°). Examples: Input: a = 4 Output: 1.65685 Input: a = 5 Output: 2.07107 Recommended: Please try your approach on first, before moving on to the solution. Repeat the process 6 more times until you’ve finished your octagon. A square has a larger area than any other quadrilateral with the same perimeter. Alternatively, each pair of the triangles forms a square of side 9 cm. The square method of constructing regular polygons offers a general procedure for constructing any regular polygon by using a square of same side as the regular polygon. Did you make this project? For more see Constructing an inscribed square. If a circle is inscribed in the square, the area of the circle is / (about 0.7854) times the area of the square. Median response time is 34 minutes and may be longer for new subjects. Share it with us! If you could show me how to solve this problem, it would be greatly appreciated. Please do Subscribe … 2. Next, draw a straight line between the ends of each neighboring set of lines in the circle to create an octagon. Construction of an octagon in a circle can be done with a compass, pencil, and a straight edge. A square tiling is one of three regular tilings of the plane (the others are the equilateral triangle and the regular hexagon). Draw straight lines between adjacent points on the circumference, and you've drawn a regular nonagon. Keywords circles , circumscribed , inscribe , constructions , construct , octagons , circumscribe , constructs These diameters were constructed by bisecting the right angles created by the horizontal and vertical diameters. The compass then steps around the circle marking off each side. Bisect the angles