Area of a Trapezium
Learn how to find the area of trapeziums, including right-angled and isosceles trapeziums. Let's get started! 🚀
Video Lesson
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Flashcards
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🛎️ What is a Trapezium?
- A trapezium is a four-sided shape with only one pair of parallel sides.
- The height is the perpendicular distance between the parallel sides.
🛎️ Area of a Trapezium
- The area of a trapezium is given by:
- Here, and are the lengths of the parallel sides.
🛎️ Area of a Right-Angled Trapezium
- A right-angled trapezium has two right angles, so the height is easy to identify.
- Use the same formula and take the perpendicular side as the height.
🛎️ Finding the Height of a Trapezium
- Use the same formula:
- Substitute the known values and solve for the height.
Practice Questions
Test your understanding
Which of the following is always true for a trapezium?
Correct! 🎉 +10 pointsNot quite right
A trapezium is defined as a quadrilateral with exactly one pair of parallel sides. Two pairs would make it a parallelogram.
What is the height of a trapezium?
Correct! 🎉 +10 pointsNot quite right
The height is always the perpendicular distance between the two parallel sides, not a slanted or longest side.
Calculate the area of a trapezium with parallel sides 5 cm and 9 cm, and height 3 cm.
Correct! 🎉 +20 pointsNot quite right
Use the formula: Area = (sum of parallel sides ÷ 2) × height. (5 + 9) ÷ 2 × 3 = 21 cm².
In a right-angled trapezium, the shorter base is 6 cm, the longer base is 18 cm, and the area is 60 cm². What is the height?
Correct! 🎉 +20 pointsNot quite right
60 = (6 + 18) ÷ 2 × height. (24 ÷ 2) = 12, so 60 = 12 × height. Height = 5 cm.
An isosceles trapezium has parallel sides of 15 cm and 9 cm. If its area is 48 cm², what is the height?
Correct! 🎉 +20 pointsNot quite right
48 = (15 + 9) ÷ 2 × height. (24 ÷ 2) = 12, so height = 48 ÷ 12 = 4 cm.
Find the area of the isosceles trapezium shown, where the bottom base is 10 cm, the top base is 20 cm, and the height is 12 cm.
Correct! 🎉 +30 pointsNot quite right
Area = (10 + 20) ÷ 2 × 12 = 30 ÷ 2 × 12 = 15 × 12 = 180 cm².
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