# Quadrilaterals - Page 6

Questions

- What is a quadrilateral that has exactly 2 congruent consecutive sides? Would it be either a parallelogram and/or a trapezoid?
- Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(7 pi)/8 # and the parallelogram's area is #18 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #36 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #64 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?
- Two opposite sides of a parallelogram each have a length of #7 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #42 #, how long are the other two sides?
- Two opposite sides of a parallelogram have lengths of #5 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #45 #, how long are the other two sides?
- How do you prove that sum of the squares on the sides of a rhombus is equal to the sum of squares on its diagonals?
- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(3pi)/8 #, what is the difference between the areas of the rhombuses?
- A rhombic prism has the diagonal of the rhombus measuring 16 and 12 cm. If the the altitude of the prism is equal in size to the side of the rhombus. What is the surface area and the volume of the Rhombic Prism?
- Two opposite sides of a parallelogram have lengths of #25 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #45 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #12 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #72 #, how long are the other two sides?
- A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #70 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #3 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?
- Pg 23, q36 How do I figure this out? thanks
- Two opposite sides of a parallelogram each have a length of #32 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #140 #, how long are the other two sides?
- Prove that if midpoints of non-parallel sides of a trapezium are joined, this line is parallel to parallel sides of the trapezium?
- My quadrilateral has congruent diagonals. What must it be?
- Two rhombuses have sides with lengths of #1 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #14 # and #11 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?
- What is a quadrilateral square?