# Isosceles Trapezoid Formula

## Isosceles Trapezoid Formula

A trapezoid with congruent base angles and congruent non-parallel sides is known as an Isosceles Trapezoid to which the  Isosceles Trapezoid Formula pertains. A quadrilateral with just one of its sides parallel is called a trapezoid. Students can distinguish an Isosceles Trapezoid Formula from other quadrilaterals owing to its numerous intriguing characteristics. They can go in-depth about the Isosceles Trapezoid Formula on the Extramarks website and mobile application.

## Isosceles Trapezoid Definition

A trapezoid that has non-parallel sides and base angles of the same size is said to be isosceles. In other terms, a trapezoid is an isosceles trapezoid if its two opposing sides (or bases) are parallel and its two non-parallel sides are of equal length. Students can look at the illustration accompanying Isosceles Trapezoid Formula on the Extramarks website and mobile application, where the bases of the trapezoid, sides a, and b, are opposite each other and sides c and d are of equal length.

### Properties of Isosceles Trapezoid

The characteristics of an Isosceles Trapezoid Formula are as follows:

• It has a symmetry axis. Isosceles Trapezoid Formula 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 above, AB II DC)
• Other than the base, the remaining sides are all non-parallel and equal in length. (In the picture shown, c = d)
• The length of the diagonals is constant. (AC = BD)
• The same holds true for the base angles. (∠D = ∠C, ∠A=∠B)
• The sum of opposite angles is 180° or supplementary. (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)

### Isosceles Trapezoid Formula

The formulas to determine the Isosceles Trapezoid Formula area and perimeter are listed below:

• Isosceles Trapezoid Formula area

The base sides or parallel sides must be added, divided by 2, and the result multiplied by the height to determine the isosceles trapezoid’s area.

• (Sum of Parallel Sides 2) h = Area of Isosceles Trapezoid
• Trapezoidal isosceles’ perimeter

Students must add each side of the isosceles trapezoid in order to get its perimeter.

• Isosceles Trapezoid perimeter equals the sum of all sides

### Area of isosceles trapezoid

One set of nonparallel sides of an isosceles trapezoid is congruent. Using the equation A + B over two times h, where A and B are the bases and h is the perpendicular height, students can calculate the area of the trapezoid.

A trapezoid that has non-parallel sides and base angles of the same size is said to be isosceles. In other terms, a trapezoid is an isosceles trapezoid if its two opposing sides (or bases) are parallel and its two non-parallel sides are of equal length.

A trapezoid with congruent base angles and congruent non-parallel sides is known as an Isosceles Trapezoid Formula. A quadrilateral with just one of its sides parallel is called a trapezoid. Owing to its remarkable characteristics, students can distinguish an Isosceles Trapezoid to which the Isosceles Trapezoid Formula pertains from other quadrilaterals.

The base sides or parallel sides must be added, divided by 2, and the result multiplied by the height to determine the isosceles trapezoid’s area.

(Sum of Parallel Sides 2) h = Area of Isosceles Trapezoid Formula

Isosceles Trapezoid Formula perimeter

In order to acquire the perimeter of an Isosceles Trapezoid, students must add each side of the isosceles trapezoid.

According to the Isosceles Trapezoid Formula, the perimeter of an Isosceles Trapezoid equals the sum of all sides.

### Examples on Isosceles Trapezoid

• Example 1: Assuming that the isosceles trapezoid has an area of 128 inches2 and bases that are 12 inches and 20 inches long, determine its height.

Solution: Given an area of 128 inches square and bases of 12 and 20 inches, one can calculate the area of an isosceles trapezoid as follows: 128 = [(12 + 20) 2]. Height is 128/16, or 8 inches.

• Example 2: Calculate the area of an isosceles trapezoid with a height of 4 inches and bases of 3 inches and 5 inches.

Solution: Given height, the bases of an isosceles trapezoid are 3 inches and 5 inches, and its height is 4 inches.

Area = [(3 + 5) ÷ 2] 4 Square Inches Equals 16 inches2

• Example 3: Assuming an isosceles trapezoid has bases of 20 and 25 inches and non-parallel sides of 30 inches each, calculate its perimeter.

Solution: The sum of all the sides of an isosceles trapezoid equals the perimeter of the trapezoid.

An isosceles trapezoid’s perimeter is equal to 105 inches (20 + 25 + 30 + 30).

### Practice Questions on Isosceles Trapezoid

Q1. Which of the following describes a trapezoid’s characteristics?

Options

A. The top and bottom bases are parallel to one another.

B. The top and bottom bases are parallel to one another.

C. Congruent angles can be found on both sides of the base.

D. Congruent angles can be found on both sides of the base.

Q2. If the isosceles trapezoid’s base angle is 30 degrees. Try and find the other Base Angle.

Answer: The base angles of an isosceles trapezoid are equal, therefore if one base angle is 30°, the other base angle will also be 30° because of this feature.

### 1. What is an Isosceles Trapezoid?

A form of trapezoid known as an isosceles trapezoid has nonparallel sides that are equal to one another. An isosceles trapezoid is a particular kind of quadrilateral in which one set of opposing sides is divided by the symmetry axis. An isosceles trapezoid has equal-sized legs and bases that are parallel to one another.

### 2. What qualities characterize an Isosceles Trapezoid?

A four-sided isosceles trapezoid has four sides. The other two sides are equal in length but not parallel to one another, whereas the two opposing sides (bases) are parallel to one another.

### 3. What Distinguishes an Isosceles Trapezoid from a Trapezoid?

A trapezoid has different-length sides and incongruent diagonals, whereas an isosceles trapezoid has non-parallel sides that are equal, base angles that are equal, congruent diagonals, and opposite angles that are supplementary.

### 4. What is the formula for an isosceles trapezoid's perimeter?

An isosceles trapezoid’s perimeter can be calculated using the following formula: The perimeter of an isosceles trapezoid equals the sum of its sides.