7
assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed
10.
The vertices of a pentagon are the five points where its sides meet. In a regular pentagon, these vertices are equidistant from the center and are evenly spaced around a circle. In general, the coordinates of the vertices can vary depending on the specific shape and size of the pentagon. For example, a regular pentagon inscribed in a unit circle has vertices at angles of (72^\circ) increments from a starting point.
To turn a circle into a pentagon, you can inscribe the pentagon within the circle. Start by drawing the circle and then divide the circle into five equal sections using angles of 72 degrees. Mark the points where these angles intersect the circle's circumference, and connect these points with straight lines to form the pentagon. This process ensures that all vertices of the pentagon lie on the circle.
A regular 5 sided pentagon is one such example of a shape having no right angles
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4
assuming this is a regular pentagon (all five sides are equal length) the center is the intersection of the intersection of perpendicular bisectors of each side and should also be the center of the circle in which it is inscribed
10.
The vertices of a pentagon are the five points where its sides meet. In a regular pentagon, these vertices are equidistant from the center and are evenly spaced around a circle. In general, the coordinates of the vertices can vary depending on the specific shape and size of the pentagon. For example, a regular pentagon inscribed in a unit circle has vertices at angles of (72^\circ) increments from a starting point.
1
If the distance from the centre of the pentagon to a vertex is r cm then the length of the arc is 0.4*pi*r cm
To turn a circle into a pentagon, you can inscribe the pentagon within the circle. Start by drawing the circle and then divide the circle into five equal sections using angles of 72 degrees. Mark the points where these angles intersect the circle's circumference, and connect these points with straight lines to form the pentagon. This process ensures that all vertices of the pentagon lie on the circle.
*Note that it is assumed you know what the terms diameter, perpendicular, bisect/bisection and intersection mean in relation to geometry. If not, they are explained in the discussion area. To construct a regular pentagon using a compass and ruler (a longer, but more precise method): # Draw a circle in which to inscribe the pentagon and mark the center point O. # Choose a point A on the circle; this will be one vertex of the pentagon. Draw the diameter line through O and A. # Construct a line perpendicular to the line OA passing through O. Mark its intersection with one side of the circle as the point B. # Construct the point C as the midpoint of O and B. # Draw a circle centered at C through the point A. Mark its intersection with the line OB(inside the original circle) as the point D. # Draw a circle centered at A through the point D. Mark its intersections with the original circle as the points E and F. # Draw a circle centered at E through the point A. Mark its other intersection with the original circle as the point G. # Draw a circle centered at F through the point A. Mark its other intersection with the original circle as the point H. # Construct the regular pentagon AEGHF. To construct a regular pentagon using a protractor (less time, but not as accurate): # Make a short line. This will be one side of the pentagon. Label the ends A and B # Place the baseline of the protractor on this line, with the centre at A. # Mark the point of 108o with a dot. # Make another line which starts at A, is the same length as AB and goes towards the dot. # Repeat the use of the protractor on the newest line you have drawn three more times. The final line should meet up with B.
A regular 5 sided pentagon is one such example of a shape having no right angles
A regular pentagon has straight sides and is closed so its a polygon. Any shape with straight sides and is closed is a polygon. Example O (circle) has curved lines so its not a polygon L (square) is open therefore it is not a polygon.
Circle