Construct a quadrilateral ABCD, when AB=5 cm, BC= 6 cm, DC= 5.5 cm, AC=4 cm and BD=4.5cm.
Is it a concave polygon??
yes, it appears to be concave
How?
Please explain
To determine if the quadrilateral ABCD is concave or not, we need to examine the interior angles of the quadrilateral.
1. Start by drawing the given quadrilateral ABCD with the given lengths as follows:
- Draw a line segment AB of length 5 cm.
- From point B, draw a line segment BC of length 6 cm.
- From point C, draw a line segment CD of length 5.5 cm.
- From point D, draw a line segment DA of length 4 cm.
- Finally, connect points A and D with a line segment AD of length 4.5 cm.
2. Label the points as A, B, C, and D, as indicated.
3. Now, to determine the interior angles of the quadrilateral ABCD, we can use the fact that the sum of the interior angles in any quadrilateral is 360 degrees.
4. Measure each of the four angles (A, B, C, and D) using a protractor or other angle measuring instrument.
5. Add up the measures of the four angles. If the sum is 360 degrees, then the quadrilateral ABCD is convex. If the sum is greater than 360 degrees or less than 360 degrees, then the quadrilateral ABCD is concave.
6. Compare the sum of the angles with 360 degrees.
If the sum of the angles is 360 degrees, then the quadrilateral ABCD is convex. Conversely, if the sum is greater than 360 degrees or less than 360 degrees, then the quadrilateral is concave.
Please follow the steps above to calculate the sum of the angles and determine if the quadrilateral ABCD is concave or not.