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## Formula for area of ​​trapezoid: normal, square, isosceles

### Formula for calculating the perimeter of a trapezoid: regular, square, isosceles

A trapezoid is a convex quadrilateral with two parallel sides that we encounter a lot in everyday life. The two parallel sides of a trapezoid are called the base edges, and the remaining sides are called the sides. If calculating the perimeter of a trapezoid is quite easy to remember, simply adding the 4 sides, the formula for calculating the area of ​​a trapezoid is a bit more difficult to remember.

There are three common types of ladders:

• Normal trapezoid
• Square trapezoid
• Isosceles trapezoid

### Formula to calculate the area of ​​a trapezoid

Definition: A trapezoid is a convex quadrilateral with two parallel base sides, the remaining two sides are called lateral sides.

You are viewing: Formula to calculate the area of ​​a trapezoid

There is a trapezoid ABCD with base length AB a, base CD b, and height h. The formula for calculating the area of ​​a trapezoid is: the average of the two bases multiplied by the height between the two bases. In there:

• S is the area of ​​the trapezoid.
• a and b are the lengths of the two base sides.
• h is the height lowered from bottom edge a to b or vice versa (distance between 2 bottom edges).

There is also a poem about calculating the area of ​​a trapezoid that is quite easy to remember as follows:

Want to calculate the area of ​​a trapezoid?

Big bottom, small bottom, we add it

Multiply by the height

Divide in half and get half anyway

For example:

A trapezoid has height = 4cm, bottom a = 5cm, big base b = 12cm. Area of ​​the upper trapezoid? Apply the formula S = hx ((a +b)/2) = 4 x ((5+12)/2)= 34 (cm).

There is also a poem about calculating the area of ​​a trapezoid that is quite easy to remember as follows:

Want to calculate the area of ​​a trapezoid?

Big bottom, small bottom, we add it

Multiply by the height

Divide in half and get half anyway.

### How to calculate the area of ​​a square trapezoid? A square trapezoid is a trapezoid with a right angle. The side perpendicular to the bases is also the height h of the trapezoid. The general formula for calculating the area of ​​a square trapezoid is similar to that of a regular trapezoid: the average of the two bases multiplied by the height between the two bases, but the height here is the side perpendicular to both bases. In there:

• S is the area of ​​the trapezoid.
• a and b are the lengths of the two base sides.
• h is the length of the side perpendicular to the two bases.

A square trapezoid ABHD has the lengths of the smallest base and the largest base being 8cm and 12cm, respectively. In which side AH = 8cm. Calculate the area of ​​that square. Apply the formula: S = hx ((a + b)/2) = 8 x ((8 + 12)/2) = 80cm.

### How to calculate the area of ​​an isosceles trapezoid? An isosceles trapezoid is a trapezoid with two equal angles adjacent to a base. The two sides of a trapezoid are equal and not parallel to each other. In addition to applying the same formula as calculating a normal trapezoid, you can also subdivide an isosceles trapezoid to calculate the area of ​​each part and then add it together. For example, an isosceles trapezoid ABCD has two equal sides AD and BC. The altitudes AH and BK, the trapezoid will be divided into 1 rectangle ABKH and 2 triangles ADH and BCK. Apply the formula for the area of ​​a rectangle for ABHK and the area of ​​a triangle for ADH and BCK then add all the areas to find the area of ​​trapezoid ABCD.

Specifically this:  For example: S = hx ((a + b)/2) = 8 x ((8+16)/2) = 96cm.

S = 2 x S.ACH + S.ABHF = 2 x 1/2 x 8 x 4 + 8 x 8 = 96cm.

### Find the length of the base of the trapezoid

Once you know the area, height, and length of one base side, you can calculate the length of the other side as follows:

AB= 2 x (SABCD/h) – CD

### Find the area of ​​a trapezoid when 4 sides are known  We have the following formula: In there:

+ a, b: are the lengths of the bottom two sides, respectively.

+ c, d: respectively the length of the two sides.

In fact, if the problem raises the question of how to calculate the 4 sides of a trapezoid when knowing 4 sides, there will be no correct answer because knowing only 4 sides, there are many cases of grinding and the area is also different, you guys. can imagine the example of a trapezoid below with 4 sides 4 5 6 9 can draw 3 different shapes with different areas. However, if the problem adds a few more facts such as calculating the area of ​​a trapezoid when the lengths of 4 sides are known and it is clear which side the base is, then the area of ​​the trapezoid can be calculated, for example we have the sides where QP, where the bottom edge P is longer and the two sides R and S. The following formula can be used to calculate the area of ​​a trapezoid: In addition, in the case of calculating the area of ​​a trapezoid, when you know the sides, you can split it into 2 triangles and 1 rectangle or add the intersection line between the 2 sides and apply Heron’s formula to calculate the area of ​​​​the triangle and calculate the area of ​​a trapezoid. The above formula is also formed from this way.

### Heron’s formula for the area of ​​a triangle

Let S be the area and lengths of the three sides of the triangle a, b and c . respectively Heron’s formula can also be rewritten with ### Notes When Solving Exercises on Calculating the Area of ​​a Trapezoid

– In the process of solving math problems, many parents and students wonder if “a trapezoid has volume or not? What is the formula for calculating the volume of an isosceles trapezoid? With this question, you will not be able to find the answer because a trapezoid is a polygon in plane geometry, with no volume like a space figure.

– At secondary school geometry, students will continue to have access to mathematical forms about trapezoids. However, the exercises at this time are not simply calculating the perimeter and area, but require deep thinking, combining the properties of angles (the sum of 2 adjacent angles to 1 base in a trapezoid is 180°), calculating properties of the sides, properties of the midline of a trapezoid, etc. However, at the elementary level, you only need to know the formulas for calculating the area of ​​a trapezoid above to be able to solve most of the problems. math in your curriculum.

### Exercises trapezoid, area of ​​trapezoid

Let ABCD be a rectangle with area 15cm2, AB = 5cm. Let E lie on the line DC with C between D and E and length DE = 7cm. Calculate the area of ​​figure ABED. Prize:

According to the given title, we have the following figure:

ABCD is a rectangle, E lies on DC so AB // DE, angle ADC = 90 degrees

=> ABED is a square trapezoid

Calculate side AD = SABCD : AB = 15 : 5 = 3cm

Therefore, Area of ​​a square trapezoid ABED = AD . (AB + DE) : 2 = 3 . ( 5 + 7) : 2 = 18cm2

For example, for a trapezoid with side length a= 20cm, side b= 14cm and the height connecting from the top to the bottom is 12cm. What is the area of ​​the trapezoid? Solution: There is a = 20 cm, b = 14 cm, h = 25 cm. Ask S=?

Based on the formula for calculating the area of ​​a trapezoid, we have:

S = hx (a +b/2) or 1/2 (a+b) xh

S = 12 x ((20 + 14)/2) or 1/2 x (20+14) x 25

S = 1/2 x 34 x 25 = 425 cm.

Thus, based on the formula for calculating the area of ​​a trapezoid, we can find the area of ​​a trapezoid equal to 425 cm.

Let ABCD be a rectangle with area 15cm2, AB = 5cm. Let E lie on the line DC with C lying between D and E and length DE = 7. Calculate the area of ​​the figure ABED.

Prize:

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

=> ABED is a square trapezoidCalculate side AD = SABCD : AB = 15 : 5 = 3cm Therefore, Area of ​​square trapezoid ABED = AD . (AB + DE) : 2 = 3 . ( 5 + 7) : 2 = 18cm2

Problem: There is a trapezoid ABCD with small base AB = 5 cm, big base DC is twice as long as the small bottom. The height of the trapezoid AH = 6 cm. Calculate the area of ​​a trapezoid. How to calculate the area of ​​a trapezoid?

Knowledge about trapezoids is quite popular with primary school students. To review problems related to calculating the area of ​​a trapezoid, please follow the information and illustrative examples right below.

First of all, we need to define what is a trapezoid? A trapezoid is a convex quadrilateral with 2 pairs of opposite sides parallel to each other and these are the 2 base sides, the other 2 opposite sides are the 2 sides. Other properties of a trapezoid include: two adjacent angles sum to 360 degrees, and the line connecting the midpoints of the two sides is called the median of the trapezoid.

Types of trapezoids include: square trapezoid (a trapezoid with 1 right angle), isosceles trapezoid (a trapezoid with 2 equal adjacent sides), isosceles right trapezoid (which is a rectangle). ## HOW TO CALCULATE THE AREA OF A TRAVALS

The formula for calculating the area of ​​a trapezoid: S = 1⁄2 h (a + b) (The area of ​​a trapezoid is half the product of the sum of the 2 bases and the height corresponding to the 2 bottom sides, the unit of area is square meters).

Formula explanation:

S: Area of ​​trapezoid

a, b: The lengths of the two bases of the trapezoid

h: Altitude length

To make it easier to remember how to calculate the area of ​​a trapezoid, you can memorize the following stanza:

Want to calculate the area of ​​a trapezoid?

Big bottom, small bottom we add in

Then multiply by the high sugar

Split the result anyway.

Below is an illustrative example to help you apply the formula for calculating the area of ​​a trapezoid.

Problem: There is a trapezoid ABCD with small base AB = 5 cm, big base DC is twice as long as the small bottom. The height of the trapezoid AH = 6 cm. Calculate the area of ​​a trapezoid.

Prize:

The math says:

AB = 5 cm

DC is twice as long as AB, so DC = 10 cm

AH = 6 cm

Immediately applying the formula for calculating the area of ​​a trapezoid, we can calculate:

S = 1⁄2 h (a + b) = 1⁄2 x 6 x (5 + 10) = 40 cm2

Question 1. Let ABCD trapezoid with height 4.2 dm, area = 36.12 dm2, and big base CD is 7.8 dm longer than the bottom AB. Extend AD and BC intersect at E. Know AD = 3/5 DE. What is the area of ​​triangle ABE?

Question 2. Let ABCD trapezoid. Four points M, N, P, Q are the midpoints of sides AB, BC, CD, DA, respectively. The area of ​​quadrilateral MNPQ is 115 cm2. Calculate the area of ​​trapezoid ABCD.

Question 3. Let ABCD be a square trapezoid (angles A, D are right angles) with AB=4cm, DC=5cm, AD=3cm. Connect D to B to get two triangles ABD and BDC.

a) Calculate the area of ​​the triangle.

b) Calculate the percentage ratio of the area of ​​triangle ABD and the area of ​​triangle BDC.

Question 4. Calculate the area of ​​a trapezoid with:

a). 8m big bottom; 75dm baby bottom; 32dm height.

b). Big bottom 1.9m; 1.3m baby bottom; 0.9m high.

c). 2/3m big bottom; baby bottom 1/2m; 3/5m high.

Question 5. Calculate the height of a trapezoid with:

a). Area 30cm²; big bottom 8cm and small bottom 0.4dm.

b). Area 6.4 dm²; 1.8dm big bottom; 1.4dm baby bottom.

c). Area 3/4m²; big bottom 1/4m and small bottom 1/8m.

Question 6. Calculate the sum of two bases of a trapezoid:

a). Area 3.6 dam²; 1.2dam height.

b). Area 3/4m²; 2/3m height.

c). Area 2400cm²; 3.8dm height.

Question 7. A trapezoidal piece of land has a small bottom of 18m and is ¾ of the big bottom. Calculate the area of ​​a trapezoid?

Question 8. A square trapezoidal field has sides perpendicular to the 2 bases, 30.5m long; large bottom 120.4m; baby bottom 79.6m.

a. Calculate the area of ​​the field in dam²

b. On average, 100dam2 yields 65.2kg of paddy. How many kilograms of rice can be obtained in the whole field?

Question 9. A trapezoid has the sum of two bases 110cm. The sum of the large bottom and the height is 114cm. The sum of baby bottom and height is 68cm. Calculate the area of ​​a trapezoid?

Question 10. A trapezoid has a small base of 2.8dm. The large base is 7/3 of the small base and 5/3 of the height. Calculate the area of ​​a trapezoid.

Question 11. A trapezoidal field has a large base of 140m and is 4/3 of the small bottom, and a height of 56.4m. It is calculated that for every 5dam², 320kg of rice can be harvested. How many tons of rice does the whole field yield?

Question 12. A trapezoidal piece of land has the sum of the large bottom, the small bottom and the height of 90m. Baby bottom is 3/4 of baby bottom; the height is ½ of the big bottom. Knowing that every 2 dam², it is necessary to fertilize 50kg of fertilizer. How many quintals of fertilizer are required to fertilize the whole field?

Question 13. A trapezoidal field has a large bottom of 75.6m; baby bottom 62.4m and height 40m. Know that 2/5 of the field is planted with corn, 1/3 of the area is planted with potatoes, and the rest is planted with peanuts. Calculate the area planted for each type of tree above?

### Formula for Calculating Trapezoid Height, Large Bottom, Small Bottom Trapezoid

With the formula for calculating the area of ​​a trapezoid above, we can also easily solve advanced exercises on trapezoids: calculate the height of a trapezoid when the area is known; Calculate the large base and the small base of a trapezoid when the area is as follows:

#### Formula to calculate the height of a trapezoid when the area and length of 2 sides are known #### The formula for the sum of the two bases of a trapezoid given the area and height Posted by: Le Hong Phong High School

Category: Education

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