Question 1: The area of a trapezium is given by the formula ½(a + b)h, where a and b are the lengths of the parallel sides and h is the height. Understanding how to correctly apply this formula is essential to avoid common mistakes.

Answer: The area is ½ times (sum of parallel sides) times height

Question 1: Calculate the area of a trapezium with parallel sides 8 cm and 12 cm, and height 5 cm.

Answer: 50

Question 2: A trapezium has bases of 10 m and 15 m, and a height of 6 m. Find its area.

Answer: 97.5

Question 3: If the area of a trapezium is 84 cm², and the parallel sides are 7 cm and 11 cm, what is the height?

Answer: 6

Question 4: Construct a trapezium with bases 9 cm and 14 cm, and a height of 4 cm. Calculate its area.

Answer: 46

Question 1: A garden has a trapezium-shaped pond with bases measuring 6 m and 10 m, and a height of 3 m. A gardener wants to surround the pond with a fence. Calculate the area of the pond and explain why understanding the formula ½(a+b)h helps in planning the fencing.

Answer: The area is 24 m². Using ½(a+b)h ensures accurate calculation of space for fencing, avoiding over- or under-estimation.

Question 2: A roofing contractor needs to calculate the area of a trapezoidal section of roof. The parallel sides are 20 m and 25 m, and the height is 8 m. Show your work and state any common mistakes students might make.

Answer: Area = ½(20+25)×8 = ½(45)×8 = 22.5×8 = 180 m². Common mistake: forgetting to divide by 2 or adding bases incorrectly.

Question 1: A trapezium-shaped field has bases of 50 m and 70 m, with a height of 30 m. How much area does the field cover? Why might accurate calculation be important for farming?

Answer: The area is 1,200 m². Accurate calculation helps in planning for seed, fertilizer, and resource allocation.

Question 1: Design a trapezium with bases in the ratio 3:5 and height 12 cm. If the total area must be 144 cm², find the lengths of the bases.

Answer: Base a = 9 cm, base b = 15 cm.

Question 2: A trapezium's area is incorrectly calculated as (a + b) × h. Explain the mistake and correct it.

Answer: The mistake is omitting the ½ factor. Correct formula: ½(a + b)h.

Question 1: A student calculates the area of a trapezium with bases 10 cm and 14 cm, height 8 cm, using the formula ½(10 + 14)×8, but gets 48 cm². Find the mistake and provide the correct answer.

Answer: The mistake is missing the division by 2; correct area = (24×8)/2 = 96 cm².

Question 2: Another student uses the formula (a + b) × h instead of ½(a + b)h. Calculate the area of a trapezium with bases 7 m and 13 m, height 4 m, using both formulas. Which is correct?

Answer: Using (a + b)×h: (7+13)×4=80; incorrect. Correct: ½(7+13)×4=½×20×4=40 m².