which of the following cannot be the area of a quadrilateral whose sides all have length 8? 1. 12 2. 36 3. 48 4. 64 5. 72

Expert Answers
baxthum8 eNotes educator| Certified Educator

A quadrilateral that is a square yields an area of 64.  Any other quadrilateral with all the sides of 8 is a rhombus.  In order to find the area of a rhombus since you know the length of side, you just need the height.  If you draw a rhombus with any dimension the side is the hypotenuse of the right triangle in order to construct the height.  Therefore, the height must always be smaller than the length of side as the hypotenuse is always the longest side of a right triangle.  So the height must be:  `h<= 8.`

Since you can find the area of a rhombus by `A = bh,`

where b will always be 8, the only area which produces a result in which would not fit these dimensions is: