An isosceles trapezoid is a trapezoid with congruent base angles and also congruent non-parallel sides. A trapezoid is a quadrilateral with only among its political parties parallel. An isosceles trapezoid has numerous interesting properties that make it distinctive and assist us differentiate it native the various other quadrilaterals. Allow us comment on them in detail.

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 1 Isosceles Trapezoid Definition 2 Properties the Isosceles Trapezoid 3 Isosceles Trapezoid Formula 4 FAQs on Isosceles Trapezoid

An isosceles trapezoid can be identified as a trapezoid in i beg your pardon non-parallel sides and base angles space of the same measure. In other words, if 2 opposite sides (bases) the the trapezoid are parallel, and also the 2 non-parallel sides are of equal lengths, climate it is one isosceles trapezoid. Look in ~ the image below-showing political parties c and also d are equal in lengths and also opposite political parties a and b (bases the the trapezoid) space parallel to each other.

Following are the properties of one isosceles trapezoid follow to the number given below.

One pair of political parties is parallel and they room the basic sides. (AB II DC in the offered image)The staying sides various other than the base are non-parallel and are equal in length. (c = d in the provided image)The diagonals are the same in length. (AC = BD)The amount of opposite angles is 180° or supplementary. (∠A + ∠C = 180° and ∠B + ∠D = 180°)

Following space the formulas to calculate the area and perimeter that the isosceles trapezoid.

Area that isosceles trapezoid

To discover the area that the isosceles trapezoid we have actually to include the base sides or parallel sides and divide that by 2 and also then main point the result with height.Area that Isosceles Trapezoid = (sum of parallel sides ÷ 2) × h

Perimeter that isosceles trapezoid

To discover the perimeter of the isosceles trapezoid we have actually to include all the political parties of the isosceles trapezoid.Perimeter that Isosceles Trapezoid = amount of every sides

Examples on Isosceles Trapezoid

Example 1: Find the height of the isosceles trapezoid if the area is 128 inches2 and also the lengths that the bases space 12 inches and 20 inches.Solution: Given area = 128 inches2 , Bases = 12 inches and also 20 incheswe know that area that isosceles trapezoid = (sum the parallel political parties ÷ 2) × heighttherefore, 128 = <(12 + 20) ÷ 2> × heightHeight = 128/16 = 8 inches
Example 2: Find the area of an isosceles trapezoid if its bases space 3 inches and 5 inches and also its elevation is 4 inches.Solution: Area that isosceles trapezoid = (sum of parallel sides ÷ 2) × heightgiven, bases = 3 inches and 5 inches, elevation = 4 inchesArea = <(3 + 5) ÷ 2> × 4Area = 16 inches2
Example 3: Find the perimeter of an isosceles trapezoid if that bases are 20 inches and 25 inches and non-parallel sides room 30 customs each.Solution: Perimeter of an isosceles trapezoid = amount of every sides of isosceles trapezoidPerimeter of one isosceles trapezoid = 20 + 25 + 30 + 30 = 105 inches
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FAQs on Isosceles Trapezoid

What is an Isosceles Trapezoid?

An isosceles trapezoid is a form of trapezoid that has nonparallel sides equal to every other. An isosceles trapezoid is a type of quadrilateral whereby the line of symmetry bisects one pair of the opposite sides. The bases of one isosceles trapezoid space parallel to each other along with the foot being equal in measure.

What room the nature of an Isosceles Trapezoid?

In one isosceles trapezoid, the variety of sides is four. The two opposite political parties (bases) space parallel to every other and the various other two sides are equal in lengths however non-parallel to every other.

If One base Angle of Isosceles Trapezoid is 30°. Discover the other Base Angle.

According come the property of one isosceles trapezoid, the basic angles room equal, as such if one base angle is 30°, climate the various other base angle will be same to 30°.

What is the Difference in between a Trapezoid and an Isosceles Trapezoid?

In a trapezoid, every side is of different lengths and the diagonals are not congruent, whereas, in an isosceles trapezoid the non-parallel sides space equal, the basic angles space equal, the diagonals room congruent and also the the contrary angles space supplementary.

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What is the Formula for Area of one Isosceles Trapezoid?

The formula to calculation the area of one isosceles trapezoid is Area = (sum of parallel political parties ÷ 2) × height.

What is the Formula because that Perimeter of one Isosceles Trapezoid?

The formula to calculate the perimeter of an isosceles trapezoid is Perimeter = sum of all sides the the isosceles trapezoid