Question 1: A rhombus has all sides equal to 6 cm. Calculate its perimeter.

Answer: 24

Question 2: If the diagonals of a rhombus are 10 cm and 24 cm, find the length of one side.

Answer: 13

Question 3: Explain why the diagonals of a rhombus bisect each other at right angles.

Answer: Because in a rhombus, the diagonals are perpendicular bisectors of each other, dividing the rhombus into four right triangles.

Question 4: Construct a rhombus with sides of 8 cm, where the diagonals are 10 cm and 16 cm. Use the grid to draw it accurately.

Answer: Student's drawing

Question 5: A rhombus has diagonals of lengths 14 cm and 48 cm. Calculate the measure of each interior angle.

Answer: Approximately 75° and 105°

Question 6: A gardener wants to plant a rhombus-shaped flower bed with diagonals of 12 m and 16 m. What is the area of the bed?

Answer: 96 square meters

Question 7: Calculate the length of a side of a rhombus if its area is 96 cm² and one diagonal is 16 cm.

Answer: 12

Question 8: Identify the mistake in this reasoning: 'Since a rhombus has all sides equal, all angles must be 90°.'

Answer: The mistake is assuming all angles are 90°, but in a rhombus, only the diagonals bisect at right angles; angles are usually not 90° unless it's a square.

Question 9: A rhombus has side length 9 cm. Its diagonals are equal in length. Find the length of each diagonal.

Answer: 12√2 cm (approximately 16.97 cm)

Question 10: Challenge: Prove that the diagonals of a rhombus are perpendicular by using coordinate geometry. (Use the grid to plot points and demonstrate.)

Answer: Student's coordinate proof