Question 1: A trapezium has parallel sides measuring 8 cm and 5 cm. The height of the trapezium is 4 cm. Calculate its area.

Answer: 26 cm^2

Question 2: If the non-parallel sides of a trapezium are both 6 cm, and the shorter base is 5 cm with a height of 4 cm, find the length of the longer base.

Answer: 8 cm

Question 3: Construct a trapezium on the grid with bases of 7 cm and 4 cm, and height of 3 cm. Label the bases.

Answer: Constructed shape with bases labeled 7 cm and 4 cm at parallel sides

Question 4: The longer base of a trapezium is 10 cm, the shorter base is 6 cm, and the height is 5 cm. What is the area of this trapezium?

Answer: 40 cm^2

Question 5: A trapezium has bases of 9 cm and 4 cm. The area is 31.5 cm^2. Find the height.

Answer: 3 cm

Question 6: A real-world scenario: A trapezium-shaped garden has parallel sides of 12 m and 8 m, with a height of 5 m. Calculate the area of the garden.

Answer: 50 m^2

Question 7: Two trapeziums have the same height and one has bases 6 cm and 4 cm, the other has bases 8 cm and 5 cm. If both have an area of 24 cm^2, find the height assuming the areas are correct.

Answer: 4 cm

Question 8: Calculate the perimeter of a trapezium with sides 5 cm, 7 cm, 6 cm, and 4 cm.

Answer: 22 cm

Question 9: A trapezium's non-parallel sides are 5 cm and 7 cm. The bases are 10 cm and 6 cm respectively. If the height is 4 cm, verify the area calculation: (area = 0.5 × (sum of bases) × height).

Answer: 32 cm^2

Question 10: Identify and correct the mistake in this statement: "The area of a trapezium is found by multiplying the sum of the bases by the height."

Answer: Incorrect; it should be 0.5 × (sum of bases) × height

Question 11: Challenge: A trapezium with bases 9 cm and 5 cm has an area of 28 cm^2. Find the height, and then verify your result.

Answer: Height = 4 cm