Isosceles Trapezoid Formula: Area & Perimeter

Isosceles Trapezoid formula is based on two components: Area of an Isosceles Trapezoid and Perimeter of an Isosceles Trapezoid

• An isosceles trapezoid has legs or non-parallel sides that are equal in length. The parallel sides (base) of the isosceles trapezoid has angles equal to one another. 
• An isosceles trapezoid is simply a form of a trapezoid that has congruent base angles and non-parallel sides.
• A trapezoid, also called a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel and opposite sides, along with a set of non-parallel sides. 
• The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a four-sided closed 2-dimensional figure, where the shortest distance between the two parallel sides, is called “Altitude”. There are three types of trapezoids:

• Right Trapezoids
• Isosceles Trapezoids
• Scalene Trapezoids

Read Also: Centroid of a Trapezoidal Formula

Key Terms: Trapezoid, Isosceles Trapezoid, Median, Bases, Rectangle, Symmetry, Altitude, Scalene Trapezoid, Right Trapezoid

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What is Trapezoid?

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A trapezoid is a quadrilateral or a polygon that has four sides. 

• A trapezoid is also often called a “Trapezium”.
• It is a polygon with only one pair of parallel sides.
• The parallel sides of the trapezium is also known as “Parallel Bases of Trapezoid”.
• The other two non-parallel sides of the trapezoid are known as the legs of the trapezoids.
• In a trapezoid, the distance between the parallel sides is termed “Altitude”.

Types of Trapezoid

There are three different kinds of trapezoids, and they are:

• Isosceles Trapezoid
• Scalene Trapezoid
• Right Trapezoid

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Properties of Trapezoid

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Some of the properties of a trapezoid are:

• The top and bottom bases in a trapezoid are parallel to one another.
• A trapezoid's opposite sides (isosceles) are equal in length.
• Both of the bases are parallel to the median.
• The median's length is equal to (a + b)/2, the average of the two bases.
• A trapezoid is referred to as a parallelogram if both pairs of opposite sides are parallel.
• A trapezoid can serve as a square if all sets of opposite sides are parallel, all sides are equal in length, and all sides are at right angles.
• A trapezoid can serve as a rectangle if its opposite side pairs are all parallel, equal in length, and at right angles to one another.

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Isosceles Trapezoid

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An isosceles trapezoid is one that has legs or non-parallel sides that are equal in length.

• The parallel sides (base) of the isosceles trapezoid have angles that are equal to one another. 
• A line of symmetry and equal lengths for both diagonals define an isosceles trapezoid.
• If the two opposite sides (bases) of the trapezoid are seen to be parallel, and the two non-parallel sides are of equal lengths, then it is known as an isosceles trapezoid. 
• The image below indicates that c and d are equal in lengths, while the opposite sides a and b (bases of the trapezoid) are parallel to one another.

Isosceles Trapezoid

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Properties of Isosceles Trapezoid

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An isosceles trapezoid has the following characteristics:

• It has a symmetry axis. An isosceles trapezoid only has one line of symmetry connecting the middle of the parallel sides and no rotational symmetry.
• The base sides are the only pair of sides that are parallel. (In the figure, AB II DC)
• Other than the base, the remaining sides are all non-parallel and equal in length. (In the image shown, c = d)

Properties of Isosceles Trapezoid

• The length of the diagonals is constant. (AC = BD)
• the same for the base angles. (∠D = ∠C, ∠A=∠B)
• 180° or supplementary is the product of all opposite angles. (A + C and B + D both equal 180 degrees)

The parallel sides' midpoints are connected by a line segment that is perpendicular to the bases. (PQ ⊥ DC)

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Isosceles Trapezoid Formula

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There are two main trapezoid formulas, they are:

1. Area of an Isosceles Trapezoid
2. Perimeter of an Isosceles Trapezoid

The formulas to determine the isosceles trapezoid's area and perimeter are listed below.

Area of Isosceles Trapezoid

To find the area of the isosceles trapezoid we have to add the base sides or parallel sides and divide it by 2 and then multiply the result with height.

Area of Isosceles Trapezoid = (sum of parallel sides/2) × h

Perimeter of Isosceles Trapezoid

To find the perimeter of the isosceles trapezoid we have to add all the sides of the isosceles trapezoid.

Perimeter of Isosceles Trapezoid = sum of all sides

Some other important formulas of trapezoid, as per the following image, include:

• Sum of bases = B + b = 2A/h
• Height = 2A/B + b
• Oblique Side Projection = p₁ = B - b/2
• Difference of bases = B - b = 2 x p₁

Isosceles Trapezoid Formula

Also Read:

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Things to Remember

• An isosceles trapezoid is a type of trapezoid with congruent base angles and non-parallel sides.
• A trapezoid, also known by the name trapezium, is a quadrilateral or a polygon with four sides
• A trapezoid has a set of parallel and opposite sides and a set of non-parallel sides. 
• The area of isosceles trapezoid is = (sum of parallel sides/2) × h
• The perimeter of an isosceles trapezoid is = Perimeter of Isosceles Trapezoid = sum of all sides.
• An isosceles trapezoid has legs or non-parallel sides that are equal in length.