How to Find the Area of ​​a Trapezoid? Calculation and Formulas

Geometry, which is famous for its difficulties in exams, is one of the nightmares of mathematics with many different question types. Everyone has felt bad about not being able to solve geometry problems at least once in high school. After this bad feeling, we spent hours asking questions, and when we finally found the answer, we consoled ourselves by saying, “Oh, it was actually very easy.”

The trapezoid is a shape that has the potential to be the protagonist of these memories. At first glance, it makes you worry, “How are we going to get out of this now?” calculate the area of ​​a trapezoid, it’s actually much simpler than it seems. Unlike complex formulas Finding the area of ​​the trapezoid We will use simple formulas.

First, let’s get to know the trapezoid:

The most important feature of the geometric shape, which at first glance resembles a rectangle, but when it is realized that the sides are not of equal length, it turns out to be trapezoidal. has 2 parallel sides is that it is. Since these edges are parallel to each other, they are actually at the beginning of many difficult problems. coming to the aid of students It is known for.

If there is a sentence that everyone knows by heart about the trapezoid, it is definitely ‘In a trapezoid, the length of the midsole is equal to half the sum of the lower sole and the upper sole. It will happen. This phrase was told to us many times by our teachers during high school.

What are the main features of the trapezoid?

• It is a different version of the quadrilateral.
• It consists of 4 sides in total.
• It has two parallel and non-parallel sides.
• In the trapezoid, the midsole length is equal to half the sum of the lower sole and the upper sole.
• The sum of the interior angles of a trapezoid is 360°.

Let’s get to the main topic: How to calculate the area of ​​a trapezoid?

• Method #1: Calculation with height and base
• Method #2: Calculation with side lengths

Method #1: Calculation with height and base

• Step #1: First, add the base lengths. Let’s assume that the lengths of the bases in our example are 8 cm and 13 cm. 8+13:21cm.
• Step #2: Set the height. Let’s say our height in this example is 7 cm.
• Step #3: Let’s multiply the height by the sum of our base length (21). This becomes 21×7:147.
• Step #4: We can find the area of ​​our trapezoid by dividing the product of length and height by two. The area of ​​our trapezoid in this example becomes 73.5 cm with the operation 147/2.
• Step^#5: If we need to convert these mathematical operations into a formula, the following formula emerges: ((AD+BC)xh)/2.

This method will actually help you with the simplest trapezoid questions. The basis of some difficult questions is actually It is solved with this method. If you have the lower and upper base lengths and the height, you can reach the area of ​​the trapezoid in seconds. OK then If we don’t have height?

Method #2: Calculate with side lengths

• Step #1: If you know the sides of the trapezoid, divide your trapezoid into 3 shapes, 1 rectangle and 2 triangles.
• Step #2: When you do step 1, the bottom and top base lengths of the rectangle you will obtain will be equal. In this way, the base lengths of the other 2 triangles will be equal to each other. In this way, determine the base lengths of the triangles.
• Step #3: Since we have 2 vertex lengths of the triangle, we can find the height of our trapezoid using the Pythagorean theorem. Since the third side of the triangle will fall at a right angle to the trapezoid, it will also be the length of the trapezoid.
• Step #4: As we said in the first method, if you have the top and bottom base lengths along with the height of the trapezoid, ((AD+BC)xh)/2. You can easily find the area with the formula.

Although it seems difficult at first glance, Pythagorean theorem Thanks to it, you can reach the area of ​​the trapezoid very easily. To reach your trapezoid area in the easiest way 2 method you can try. The shape of the trapezoid, its properties and to the difficulty of the problem There may be changes in these 2 formulas depending on the

In this content how to calculate the area of ​​a trapezoid We demonstrated it through 2 methods.

Every shape we deal with while solving geometry problems has the potential to challenge you. To overcome these difficulties, you can also take a look at the content we have prepared about other shapes: