Geometry, the art of shapes and spaces, unveils the wonders of trapeziums, a four-sided figure with two parallel sides and two non-parallel sides. One of the fundamental aspects of exploring trapeziums lies in understanding their area—a measure that encapsulates the space they occupy on the geometric canvas.
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What Is the Area of Trapezium?
The area of a trapezium represents the space enclosed within its four sides. It is the magnitude of the region covered, providing a quantitative measure of the geometric entity. Calculating the area of a trapezium involves a formula that considers the lengths of its bases and the perpendicular distance between them.
Area of Trapezium Formula
The formula to compute the area (A) of a trapezium is elegantly expressed as:
A = \(\frac{1}{2}h(a + b)\)
where:
- h is the height, the perpendicular distance between the parallel bases,
- a and bb are the lengths of the two parallel bases.
How to Find the Area of Trapezium
The process of finding the area of a trapezium involves a systematic approach:
1. Identify the Bases
Recognize the two parallel sides of the trapezium, termed as bases.
2. Measure the Height
Determine the perpendicular distance (hh) between the bases. This is the height of the trapezium.
3. Apply the Formula
Utilize the area formula A = \(\frac{1}{2}h(a + b)\) , where aa and bb are the lengths of the bases.
4. Calculate
Perform the calculations to derive the numerical value of the trapezium’s area.
Solved Examples on the Area of Trapezium
Example 1:Consider a trapezium with bases a = 8 units and b = 12 units. The height (h) measures 5 units.
A = \(\frac{1}{2}(5)(8 + 12)\)
A =\(\frac{1}{2}(5)(20)\)
A = \(\frac{1}{2}(100)\)
A = \(50 \, \text{square units}\)
Example 2:Imagine another trapezium with bases a = 10 units and b = 14 units. The height (h) is 6 units.
A = \(\frac{1}{2}(6)(10 + 14)\)
A = \(\frac{1}{2}(6)(24)\)
Area of Trapezium = \(\frac{1}{2}(144)\)
A = \(72 \, \text{square units}\)
Here, the area of the trapezium is 72 square units.
