Question 1: Calculate the length of the longer base of a trapezium if the shorter base is 5 cm, the non-parallel sides are each 7 cm, and the height is 4 cm.

Answer: 9 cm

Question 2: Find the perimeter of a trapezium with bases of 6 cm and 10 cm, and non-parallel sides of 5 cm and 7 cm.

Answer: 28 cm

Question 3: A trapezium has bases of lengths 8 cm and 12 cm, and the height is 5 cm. Calculate its area.

Answer: 50 cm^2

Question 1: A trapezium has bases of 9 cm and 15 cm, and the non-parallel sides are equal in length. If the height is 6 cm, find the length of the equal non-parallel sides.

Answer: 10 cm

Question 2: Construct a trapezium with bases of 7 cm and 13 cm, and legs of 6 cm each. Calculate its area.

Answer: 70 cm^2

Question 1: A garden design involves a trapezium-shaped pond with bases of 4 m and 10 m, and a height of 3 m. If the pond's sides are lined with stones costing $15 per meter, what is the total cost of lining the pond?

Answer: $180

Question 1: Prove that the area of a trapezium can be derived from dividing it into a rectangle and two triangles, then derive the formula for its area.

Answer: Area = 1/2 (a + b) * height

Question 2: A trapezium with bases 12 cm and 20 cm has non-parallel sides of 8 cm and 10 cm. Calculate its area and perimeter.

Answer: Area = 164 cm^2, Perimeter = 50 cm

Question 1: A student calculates the area of a trapezium as (a + b) * height, forgetting to multiply by 1/2. Explain why this is incorrect and provide the correct formula.

Answer: Because the formula for the area of a trapezium is 1/2 (a + b) * height, not (a + b) * height alone.