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What is Area of a Trapezium?
Grade Level:
Class 7
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The area of a trapezium is the total space enclosed within its boundaries. A trapezium is a quadrilateral (a four-sided shape) with at least one pair of parallel sides. We calculate its area using a special formula that considers the lengths of these parallel sides and the perpendicular distance between them.
Simple Example
Quick Example
Imagine you have a small plot of land near your village that looks like a trapezium. One side facing the road is 10 meters long, and the parallel side behind it is 8 meters long. The distance from the road to the back of the plot is 5 meters. To find out how much space this plot covers for farming, you would calculate its area.
Worked Example
Step-by-Step
Let's find the area of a trapezium where the parallel sides are 6 cm and 10 cm, and the perpendicular distance (height) between them is 4 cm.
---STEP 1: Identify the lengths of the parallel sides (a and b) and the height (h).
Here, a = 6 cm, b = 10 cm, h = 4 cm.
---STEP 2: Write down the formula for the area of a trapezium.
Area = (1/2) * (a + b) * h
---STEP 3: Substitute the values into the formula.
Area = (1/2) * (6 + 10) * 4
---STEP 4: First, add the lengths of the parallel sides.
Area = (1/2) * (16) * 4
---STEP 5: Multiply the sum by the height.
Area = (1/2) * 64
---STEP 6: Finally, divide by 2.
Area = 32
---ANSWER: The area of the trapezium is 32 square cm (cm^2).
Why It Matters
Understanding the area of a trapezium helps engineers design bridges and buildings, as many structural components have this shape. Urban planners use it to calculate land areas for parks or housing projects. Even in computer graphics, these calculations help render realistic 3D shapes, connecting to fields like AI/ML and Computer Science.
Common Mistakes
MISTAKE: Adding only one parallel side to the height in the formula. | CORRECTION: Remember to add BOTH parallel sides (a + b) first, before multiplying by half and the height.
MISTAKE: Using a slanted side's length instead of the perpendicular height. | CORRECTION: The 'height' (h) must always be the perpendicular distance between the two parallel sides, forming a 90-degree angle.
MISTAKE: Forgetting to include (1/2) in the formula. | CORRECTION: The formula is (1/2) * (a + b) * h. Always remember the 'half' part!
Practice Questions
Try It Yourself
QUESTION: A trapezium has parallel sides of length 7 meters and 13 meters. The height is 5 meters. What is its area? | ANSWER: 50 square meters (m^2)
QUESTION: The area of a trapezium is 48 cm^2. If its parallel sides are 9 cm and 7 cm, what is its height? | ANSWER: 6 cm
QUESTION: A roadside dhaba wants to put a new roof. The roof is shaped like a trapezium with parallel edges measuring 15 feet and 25 feet. If the perpendicular distance between these edges is 10 feet, and the cost of roofing material is Rs. 50 per square foot, what will be the total cost of the roof? | ANSWER: Rs. 10,000
MCQ
Quick Quiz
Which of these is the correct formula for the area of a trapezium?
(a + b) * h
(1/2) * a * b * h
(1/2) * (a + b) * h
a * b * h
The Correct Answer Is:
C
Option C is correct because the area of a trapezium is found by taking half the sum of its parallel sides (a and b) and multiplying it by its perpendicular height (h). The other options are incorrect formulas.
Real World Connection
In the Real World
Many bridges, like the iconic Bandra-Worli Sea Link in Mumbai, have sections that resemble trapeziums. Civil engineers and architects use the area of a trapezium to calculate the amount of material needed for construction, ensuring stability and cost-effectiveness. Even the design of some mobile phone screens or TV panels might involve trapezoidal shapes.
Key Vocabulary
Key Terms
TRAPEZIUM: A quadrilateral with at least one pair of parallel sides. | PARALLEL SIDES: Sides that are always the same distance apart and never meet. | HEIGHT: The perpendicular distance between the two parallel sides. | AREA: The amount of surface enclosed by a 2D shape. | QUADRILATERAL: A polygon with four sides.
What's Next
What to Learn Next
Great job understanding the area of a trapezium! Next, you can explore the 'Area of a Rhombus and Square' or 'Area of a Polygon'. These concepts will build on your understanding of quadrilaterals and help you calculate areas of even more complex shapes.
