Properties Of A Isosceles Trapezoid

Contents

1 Isosceles Trapezoid
2 Isosceles Trapezoid Definition
3 Properties of Isosceles Trapezoid
4 Isosceles Trapezoid Formula
- 4.1 Expanse of isosceles trapezoid
- 4.2 Perimeter of isosceles trapezoid
- 4.3 Related Articles on Isosceles Trapezoid
5 Examples on Isosceles Trapezoid
6 Practise Questions on Isosceles Trapezoid
7 FAQs on Isosceles Trapezoid
- vii.1 What is an Isosceles Trapezoid?
- 7.2 What are the Backdrop of an Isosceles Trapezoid?
- 7.3 If I Base of operations Bending of Isosceles Trapezoid is xxx°. Notice the Other Base Angle.
- 7.four What is the Difference Between a Trapezoid and an Isosceles Trapezoid?
- seven.5 What is the Formula for Area of an Isosceles Trapezoid?
- 7.6 What is the Formula for Perimeter of an Isosceles Trapezoid?
- 7.vii Isosceles Trapezoid- Formula, Backdrop, Definition, Examples

Isosceles Trapezoid

An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that arrive unique and assist us differentiate it from the other quadrilaterals. Let us talk over them in particular.

Isosceles Trapezoid Definition

An isosceles trapezoid tin can be defined as a trapezoid in which not-parallel sides and base of operations angles are of the aforementioned measure. In other words, if two opposite sides (bases) of the trapezoid are parallel, and the two not-parallel sides are of equal lengths, then it is an isosceles trapezoid. Look at the image beneath-showing sides c and d are equal in lengths and opposite sides a and b (bases of the trapezoid) are parallel to each other.

Isosceles Trapezoid ABCD

Backdrop of Isosceles Trapezoid

Following are the properties of an isosceles trapezoid according to the figure given below.

Properties of Isosceles Trapezoid

It has an axis of symmetry. It has no rotational symmetry and one line of symmetry joining the midpoint of the parallel sides.
One pair of sides is parallel and they are the base sides. (AB II DC in the given image)
The remaining sides other than the base are non-parallel and are equal in length. (c = d in the given image)
The diagonals are the same in length. (Air conditioning = BD)
The base of operations angles are the same. (∠D = ∠C, ∠A=∠B)
The sum of contrary angles is 180° or supplementary. (∠A + ∠C = 180° and ∠B + ∠D = 180°)
The line segment joining the midpoints of the parallel sides is perpendicular to the bases. (PQ ⊥ DC)

Isosceles Trapezoid Formula

Following are the formulas to calculate the area and perimeter of the isosceles trapezoid.

Area of isosceles trapezoid

To find the area of the isosceles trapezoid we take to add the base sides or parallel sides and split it by 2 then multiply the consequence with summit.
Area of Isosceles Trapezoid = (sum of parallel sides ÷ 2) × h

Perimeter of isosceles trapezoid

To find the perimeter of the isosceles trapezoid nosotros have to add together all the sides of the isosceles trapezoid.
Perimeter of Isosceles Trapezoid = sum of all sides

Isosceles Trapezoid Formulas

Examples on Isosceles Trapezoid

Instance one:
Notice the height of the isosceles trapezoid if the area is 128 inches²
and the lengths of the bases are 12 inches and 20 inches.
Solution:
Given area = 128 inches^two
, Bases = 12 inches and xx inches
we know that surface area of isosceles trapezoid = (sum of parallel sides ÷ ii) × superlative
therefore, 128 = [(12 + 20) ÷ 2] × height
Summit = 128/xvi = 8 inches
Instance 2:
Notice the area of an isosceles trapezoid if its bases are 3 inches and 5 inches and its superlative is four inches.
Solution:

Surface area of isosceles trapezoid = (sum of parallel sides ÷ two) × meridian
given, bases = iii inches and 5 inches, height = four inches
Area = [(3 + 5) ÷ 2] × four
Area = sixteen inches²
Instance three:
Find the perimeter of an isosceles trapezoid if its bases are 20 inches and 25 inches and non-parallel sides are 30 inches each.
Solution:
Perimeter of an isosceles trapezoid = sum of all sides of isosceles trapezoid
Perimeter of an isosceles trapezoid = 20 + 25 + 30 + 30 = 105 inches

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Practice Questions on Isosceles Trapezoid

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FAQs on Isosceles Trapezoid

What is an Isosceles Trapezoid?

An isosceles trapezoid is a type of trapezoid that has nonparallel sides equal to each other. An isosceles trapezoid is a type of quadrilateral where the line of symmetry bisects one pair of the opposite sides. The bases of an isosceles trapezoid are parallel to each other along with the legs existence equal in measure.

What are the Backdrop of an Isosceles Trapezoid?

In an isosceles trapezoid, the number of sides is 4. The two opposite sides (bases) are parallel to each other and the other two sides are equal in lengths but not-parallel to each other.

If One Base Angle of Isosceles Trapezoid is 30°. Find the Other Base Bending.

According to the holding of an isosceles trapezoid, the base of operations angles are equal, therefore if one base of operations angle is thirty°, then the other base angle will be equal to thirty°.

What is the Difference Between a Trapezoid and an Isosceles Trapezoid?

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

What is the Formula for Area of an Isosceles Trapezoid?

The formula to summate the area of an isosceles trapezoid is Area = (sum of parallel sides ÷ two) × height.

What is the Formula for Perimeter of an Isosceles Trapezoid?

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