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Area of Trapezoid: Formula, Properties, Theorems & Derivation with Examples

Area of Trapezoid

Unlike Square and Rectangle, the Trapezoid also has four sides but its two sides are non-parallel. That is why the formula, Properties, Theorems & Derivation of Area of Trapezoid is also different from these 4 sided Figures.

Here we the team members of recruitmentresult.com are going to discuss about the Formula, Properties, and Theorems & Derivation for Area of Trapezoid along with Examples. If you are searching for same take a glance over the whole page…

Area of Trapezoid

The area of a trapezoid is given by the formula:

Area = h* (b1+b2 / 2)

where

  • b1, b2 are the lengths of each base
  • h is the altitude (height)

Area of Trapezoid

Recall that the bases are the two parallel sides of the trapezoid. The altitude (or height) of a trapezoid is the perpendicular distance between the two bases.

Check Formula To Find Area Of A Trapezium: Area Of A Trapezium

Some Examples on Problems on Area of a Trapezoid:

Question 1: Find the area of a trapezoid whose parallel sides are 24 cm and 20 cm and the distance between them is 15 cm.

As given in the question:

B1= 24 cm

B2= 20 cm

H= 15 cm

Area of trapezoid= h* (b1+b2 / 2)

Putting the values = 15*(44/2)

= 15*22 = 330 cm²

Also Get Here: Area of Semicircle Formula

Question 2: Find the area of a trapezoid m whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them is 16 cm.

As given in the question:

B1= 38.7 cm

B2= 22.3 cm

H= 16 cm

Area of trapezoid formula= h* (b1+b2 / 2)

Putting the values = 16*(61/2)

= 16*30.5 = 488 cm²

Question 3: The area of a trapezoid m is 1080 cm². If the lengths of its parallel sides are 55.6 cm and 34.4 cm, find the distance between them.

As given in the question:

B1= 55.6 cm

B2= 34.4  cm

H= —

Area = 1080 cm².

Area of trapezoid= h* (b1+b2 / 2)

Putting the values =

1080 cm².= h*(90/2)

1080 cm²= 45h

H = 1080 cm²/45

= 24 cm

Get Methods with Examples: Area of Ellipse Formula

Question 4: The area of a trapezoid is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, find the other.

As given in the question:

B1= 84 cm

B2= —

H= 26 cm

Area= 1586 cm²

Area of trapezoid= h* (b1+b2 / 2)

Putting the values =

1586 cm² = 26*((84 + b2)/2)

1586 cm²= 13 (84+b)

1586 cm²= 1092 + 13 b

13b = 1586-1092

13b = 494

B= 494/13

= 38 cm

Do you want to know that how the Formula of Area of Trapezoid Originated, here we have given the Derivation of area of a Trapezoid, take a look…

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

Derivation of Trapezoid

Derivation of Area of Trapezoid by creating a parallelogram from two congruent trapezoids, the formula is simply one half the area of this parallelogram.

  1. Start with a trapezoid with known base lengths (b1, b2) and altitude (height).
  2. Make a copy of it.
  3. Rotate the copy 180°.
  4. Translate (move) the copy to touch the original.

When the two trapezoids are combined in this way, the result is a parallelogram, which has two pairs of opposite, congruent sides as:

Derivation of Trapezoid

Recall that the area of a parallelogram is its altitude (h) times the length of either base. From the figure above we see that both base lengths are equal to b1+b2. So the area of the parallelogram is

Parallelogram area=(b1+b2)·h

Since this is the area of two trapezoids we have to divide this by two, giving

Trapezoid area=(b1+b2)h2

Also Get Here: Volume And Surface Area Questions And Answers

Finally..

This can be rearranged into more familiar forms: 1/2h(b1+b2) or ((b1+b2)/2) ·h

We hope with the help of details available here about Area of Trapezoid, candidates can solve the problems related to this polygon with ease. Still if aspirants have any query in their mind then they may mention their comments in below given comment box.

Something That You Should Put an Eye On

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Surface Area of SphereSurface Area of Cube Formula
Area of an Equilateral TriangleQuantitative Aptitude Quiz
Find Area of CircleSurface Area Of Cylinder
How to Find the Area of a Sector?Area Of Parallelogram

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