Formulas for finding the area of trapezoids: regular, isosceles, and square

The formula for calculating the area of a trapezoid, as well as formulas for finding the area of a triangle, are quite simple and have almost become common formulas that many students apply to solve basic geometry problems. Below are the most common trapezoid problems to help you remember this important knowledge.

Ways to calculate the area of a trapezoid

However, in many cases, not everyone understands and knows how to calculate the area of a trapezoid correctly as well as how to apply it in practice.

How to calculate the area of a trapezoid, formulas for finding the area of a regular, square, and isosceles trapezoid
 

1. What is a trapezoid? 

Trapezoid is a convex quadrilateral with two parallel sides, and the other two sides are called the legs.
In addition to the general definition, trapezoids are also divided into special cases as follows:
- Right trapezoid: A trapezoid with one right angle.
- Isosceles trapezoid: A trapezoid with two adjacent angles equal.
- Parallelogram: A trapezoid with opposite sides parallel and equal.

Details on definitions, properties, and identification on Wikipedia are all updated, you can refer to the Wikipedia article on trapezoids to understand more, and then apply the formulas effectively. 
 

2. Formulas for calculating the area of a trapezoid

* General formula: S = h x ((a + b)/2)

Where:

+ S: trapezoid area.
+ h: height from the top to the base of the trapezoid.
+ a and b: the two base sides of the trapezoid.

* Formula for calculating the area of a trapezoid when knowing 4 sides (advanced problem): In the case where the problem gives data knowing the length of 4 sides, clearly stating the base sides a, c with the base side c greater than the base side a, the side lengths b and d then you can calculate the area of the trapezoid according to the following formula.

Formula for calculating the area of a trapezoid when knowing 4 sides

Where:

S: Area.
a: smaller base side.
c: larger base side.
b, d: side lengths of the trapezoid.

* Formula for calculating the area of a right trapezoid

Where:

- S: Trapezoid area.
- a and b: Lengths of the two bases.
- h: Length of the side perpendicular to the two bases.

* Formula for calculating the area of an isosceles trapezoid

For an isosceles trapezoid, besides calculating using the general formula, you can calculate the area of trapezoid ABCD by calculating the area of each small part and then adding them together.

3. Formula for calculating the height of a trapezoid, the large base, the small base of the trapezoid

With the formula for calculating the area of a trapezoid above, we can also easily solve advanced exercises about trapezoids: finding the height of the trapezoid when knowing the area; finding the large base, small base of the trapezoid when knowing the area as follows:

4. Type b trapezoid exercises

Example for a trapezoid with the lengths of the base sides a= 20cm, b= 14cm and the height from the top of the trapezoid to the base is 12cm. What is the area of the trapezoid?

Solution: Given a = 20 cm, b = 14cm, h =25cm. Find S = ?
Based on the formula for calculating the area of a trapezoid, we have:
S = h x (a + b/2) or 1/2 (a + b) x h.
S = 25 x ((20 + 14)/2) or 1/2 x (20 + 14) x 25.
S = 1/2 x 34 x 25 = 425 (cm²).

So, based on the method of calculating the area of a trapezoid, we can find that the area of the trapezoid is 425 cm².
 

5. Notes when solving exercises about calculating the area of a trapezoid

During the process of solving math problems, many parents and students often wonder, 'Can a trapezoid have volume? How do you calculate the volume of an isosceles trapezoid?' Unfortunately, the answer to this question cannot be found because a trapezoid is a polygon in plane geometry and does not have volume like solid figures.

In secondary school geometry, students will continue to encounter various problems related to trapezoids. However, these exercises are not simply about calculating perimeter and area but require deep thinking, incorporating angle properties (the sum of two adjacent angles on one base in a trapezoid equals 180°), properties of the sides, properties of the midsegment of a trapezoid, etc. Nevertheless, at the elementary level, students only need to grasp the above-mentioned formulas for finding the area of a trapezoid to solve most of the problems in their curriculum.

Exercise 6

Problem 1: Given rectangle ABCD with an area of 15cm² and AB = 5cm. Let E lie on line DC such that C is between D and E, and DE = 7. Find the area of quadrilateral ABED.

Solution:

According to the given problem, we have the following diagram:
ABCD is a rectangle, E lies on DC so AB // DE, angle ADC = 90 degrees.

=> ABED is a right trapezoid.
AD = Area of ABCD : AB = 15 : 5 = 3 (cm).
Therefore, Area of right trapezoid ABED = AD . (AB + DE) : 2 = 3 . ( 5 + 7) : 2 = 18 (cm²).

Note:

Students can practice more trapezoid exercises for grade 5 to get familiar with this geometry, remember the formula for calculating trapezoid area effectively.

Here is a detailed and understandable guide on how to calculate the area of a trapezoid. You can apply this method to solve math problems quickly. Remember, there are various types of problems related to calculating the area of a trapezoid. However, having a general formula will help you tackle more complex geometric problems, such as finding the area of a right trapezoid when knowing the lengths of its 4 sides. The formula has been shared and referenced on Mytour.

Calculating the perimeter of a trapezoid is one of the most common exercises for students. Refer to the formula for calculating the perimeter of a trapezoid on Mytour to understand and apply it to real-life exercises.

Mytour has introduced to you the formula for calculating the area of a trapezoid. The formula for calculating the area of a triangle has also been introduced by Mytour. You can refer to them to supplement this important geometric knowledge.

Trapezoids and rectangles share many similarities. However, the methods for calculating their areas are different. You have learned how to calculate the area of a trapezoid from the content above. But what about calculating the area of a rectangle? Refer to the method introduced by Mytour to know the most accurate formula for calculating the area of a rectangle.

A square is considered the most special geometric shape among quadrilaterals. Students need to understand formulas related to squares such as the formula for calculating the area of a square and the formula for calculating the perimeter of a square, which are all very important pieces of knowledge.

For those who often work on math exercises in Word, knowing the formula for calculating the area of a trapezoid is as important as learning how to insert mathematical formulas in Word because this formula is widely used in complex geometric problems.