An issue for mathematics students, Trapezoid, which throws complex problems at various angles, is a must-need topic to solve. Bombarded by the angles and formulas that are required to solve mathematical problems, it is essential to have a grasp of such a topic, which most don’t have. Hence, in this blog, the question is, What is the Area of A Trapezoid? And various other related aspects will be answered in detail.
Definition of A Trapezoid
In simple terms, a trapezoid is a quadrilateral (with four sides) that has at least one pair of parallel sides. Bases, these parallel sides are known by this name and the other two non-parallel sides are called legs.
Moreover, there are two types of trapezoids that you will come across:
- A right trapezoid consists of two right angles.
- An isosceles trapezoid consists of non-parallel sides of equal length, and its base angles are equal.
How To Find Out The Area of A Trapezoid?
In the initial stages, it might seem that it is quite complex to find out about the Area of A Trapezoid. Don’t make the effort of memorising it, instead do this:
Generate A Copy
Begin by taking a copy of your trapezoid and placing it right next to the original one. Now, you have two trapezoids (original and copy).
Flip And Connect Trapezoids
It is now time to rotate the copied trapezoid upside down. This means the base should be on the top and connect both of them. Both of them will fit perfectly. The shape that you get now is a parallelogram.
Know Parallelogram’s Base & Height
If you look closely, you have a new base and a new height. Hence, the parallelogram’s base is:
New Base = Base1 + Base2
Moreover, since you have connected both of them, there are no changes to the new height.
Height = Original height of trapezoid
Apply Parallelogram’s Formulae
Now, you have the area of a parallelogram.
Area of Parallelogram = (Base1 + Base2) * Height
But weren’t you here to calculate the surface area of a trapezoidal prism? Wait, there is a final step.
Locate Trapezoid’s Formula
Remember, the exercise where we connected to trapezoids, this makes the area of the trapezoid half of the parallelogram.
In simple terms,
Area of the trapezoid = ½ * area of parallelogram = ½ * (Base1 + Base2) * height
And hence, this is the formula that you have been looking for.
Area of trapezoid = ½ * (Base1 + Base2) * height
We know that this is a lengthy way to understand this simple formula. But on the flip side, it is better than just reciting the formula, and you will remember this more effectively.
How Can You Find The Area of A Trapezoid? Explained With Examples
- Q) Find the area of trapezoid: base1 = 10, base2 = 7, and height = 12
Ans) Area of trapezoid = ½ * (base1 + base2) * height
= ½ * (10 + 7) * 12
The answer comes out to be 102.
- Q) Find the area of trapezoid: base1 = 7, base2 = 10, and height = 11
Ans) Area of trapezoid = ½ * (base1 + base2) * height
= ½ * (7 + 10) * 11
The answer is 93.5
Mistakes You Must Avoid While Calculating The Area of A Trapezoid
Understanding various mathematical calculations and concepts can be a bit frustrating when trying to specifically remember and apply the area of the trapezoid. Therefore, you must watch out for these mistakes and avoid them at all costs, even during exams.
Confusing Height With Slant (Leg)
A common mistake that most of you will fall for is confusingly mixing the height with the slant (leg) of the trapezoid. This can be a bit confusing as both aspects of this shape might look similar when put in a certain position. Hence, remember, height is the vertical distance between the two parallel bases and not the length of the side.
Forgetting To Divide By 2
The area of the shape consists of dividing, adding, and multiplying. However, many do add the bases and multiply them by height, but forget to divide them by 2. As mentioned in this blog, the trapezium’s formula is derived from that of the parallelogram; dividing the result by 2 is essential. Somehow, if you get lost in this mess, you can always connect with the Assignment Writers.
Using Wrong Sides As Bases
A second error is selecting the wrong two sides as bases. You only use the parallel sides as base 1 and base 2 in the area formula. Remember, the keyword here is parallel sides. Choosing non-parallel sides to calculate the area yields incorrect results, which can make the matter worse.
Skipping Units In The Final Answer
Though students may perform the calculation correctly, they may also forget to add the proper units in their final answer. Since area is measured in square units (cm², m², etc.), it is common for students to forget that they need a square unit or leave out the units altogether.
Inconsistent Use of Units
If the lengths of the bases and height are in different units (such as meters and centimetres), you will need to convert to the same unit before using the formula. Not converting the measurements will result in an incorrect area and incorrect units in your answer. This is a crucial segment that is answered in detail through Math Assignment Help.
Real Life Examples & Applications Using Trapezoids
Trapezoids aren’t just any shape in the world of mathematics. They are a critical chapter that holds regard in the physical world as well. Some of the real-life examples in which it is used include:
Architecture & Construction
In architecture and construction, the total surface area of a trapezoidal prism plays a crucial role in skyscrapers and unique designs. The trapezoidal shapes can be witnessed in building designs, windows, ramps, roofing, and structures. The complete knowledge of how to calculate the trapezoid’s area gives an estimate to the architect about the amount of material to be used.
Land Measurement
Land surveyors often encounter irregular shapes of land that look like trapezoids. The trapezoid formula is useful when plotting boundaries or figuring out the area of a piece of property. Good measurements are required in legal documents, construction planning, and selling property.
Engineering & Design
Engineers frequently use trapezoidal shapes in mechanical and civil design, particularly in ramps, support structures, and bridges. Shapes of trapeziums enable structural integrity and efficient weight distribution. This, therefore, makes calculating the area of a trapezoidal shape useful when trying to understand load capacity and the amount of raw material to use for construction.
Crafts & DIY Projects
In woodworking, tiling, or home improvement, you will commonly end up working with trapezoidal shapes. If you are constructing a bookshelf with angled sides, with the pre-determined knowledge of the area of the trapezoid, you can buy an appropriate amount of materials. This not only reduces waste and saves time, but it also preserves your money on small, but meaningful projects.
Conclusion
Calculating the Area of A Trapezoid goes beyond simply remembering a formula. It's about understanding how the shape behaves in terms of its shape and use in the larger framework of geometry as well as real-world contexts. This blog strives to clarify the content from a brief, basic definition of the trapezoid to even providing a simple way to understand the area, step by step.
