Isosceles Trapezoid Formulas (original) (raw)

Last Updated : 23 Jul, 2025

**Trapezoid is a quadrilateral in which a pair of opposite sides are parallel. It is also known as Trapezium. There are three types of Trapezoids and the Isosceles Trapezoid is one of these type. The types of Trapezoids are:

  1. Right Trapezoid
  2. Isosceles Trapezoid
  3. Scalene Trapezoid

Table of Content

Isosceles Trapezoid

Isosceles Trapezoid is a trapezium with congruent base angles and congruent non parallel sides. A trapezium is called an Isosceles trapezoid when two opposite sides (Bases) are parallel and the other two sides (legs) are of the same length.

trapezium1

Trapezium_shape

Area and Perimeter are the formulas of Isosceles Trapezoid.

Area of Isosceles Trapezoid

The area of the Isosceles Trapezoid can be calculated by adding the lengths of two parallel sides (bases) and dividing this by 2 and multiplying the result with the height of the trapezium to get the area. The area formula is given by-

**Area = ((a+b)/2) × h

Where,

a, b are the length of parallel sides

and h is the height.

To get more understanding let's solve a few examples

Sample Problems on Area of Isosceles Trapezium

**Question 1: What is the area of isosceles trapezium if the length of parallel sides are 7cm, 5cm and height is 4cm.

**Solution:

Given

Length of parallel sides (a) = 7cm, b = 5cm

Height (h) = 4cm

Area = ((a + b)/2) × h

= ((7 + 5)/2) × 4

= (12/2) × 4

= 6 × 4

= 24 cm2

**Area of given isosceles trapezoid is 24cm 2 .

**Question 2: Find the **height of isosceles trapezium if the length of parallel sides are 6cm, 4cm and area is 24cm 2 .

**Solution:

Given

Length of parallel sides (a) = 6cm, b = 4cm

Area = 24cm2

Area = ((a+b)/2) × h

24 = ((6+4)/2) × h

24 = (10/2) × h

24 = 5 × h

h = 24/5

= 4.8cm

**So from given area, base lengths the height of an isosceles trapezium is 4.8cm

Perimeter of Isosceles Trapezoid

The perimeter of an isosceles trapezoid can be calculated by adding all sides of the trapezoid. The perimeter formula is given by-

**Perimeter = a+b+c+d

Where,

a,b are lengths of two parallel sides

c,d are length of two unparallel sides

**Note: For isosceles trapezoid c = d (Unparallel side lengths are equal)

Let's look into a few examples to get more understanding.

Sample Problems on Perimeter of Isosceles Trapezoid

**Question 1: What is the perimeter of an **isosceles trapezoid if the length of sides are 7cm, 5cm, 3cm, 3cm.

**Solution:

Given,

Length of parallel sides (a) = 7cm, (b) = 5cm

Length of un parallel sides (c) = 3cm, (d) = 3cm

Perimeter = a + b + c + d

= 7+5+3+3

= 18cm

**So perimeter of given isosceles trapezium is 18cm.

**Question 2: What is the perimeter of an **isosceles trapezoid if the length of parallel sides are 8cm, 4cm and length of sides of equal lengths 2cm.

**Solution:

Given,

Length of parallel sides (bases) (a) = 8cm, (b) = 4cm

Length of un parallel sides (legs) (c) = 2cm, (d) = 2cm

Perimeter = a + b + c + d

= 8 + 4 + 2 + 2

= 16cm

**So perimeter of given isosceles trapezium is 16cm.

**Question 3: What is the area and perimeter of an isosceles trapezium with base lengths are 3cm, 6cm and the length of the **other 2 sides which are equal in length is 2.5cm and height is 1.5cm.

**Solution:

Given

Length of bases (a) = 6cm, (b) = 3cm

Length of legs i.e., sides with equal lengths (c) = 2.5cm, (d) = 2.5cm

Height (h) = 1.5cm

Area =((a+b)/2) × h

= ((6+3)/2) × 1.5

= (9/2) × 1.5

= 4.5 × 1.5

= 6.75cm2

Perimeter = a + b + c + d

= 6 + 3 + 2.5 + 2.5

= 14cm

**So for the given data, Area is 6.75cm 2 & perimeter is 14cm.

Practice Problems

**Problem 1: Given an isosceles trapezoid with bases a=10 units and b=6 units and height of the trapezoid is 8 units. Find the length of the non-parallel sides.

**Problem 2: The area of an isosceles trapezoid is 144 square units with bases measuring 12 units and 8 units. Calculate the height of the trapezoid.

**Problem 3: In an isosceles trapezoid the length of one of the legs is 13 units and the lengths of the bases are 16 units and 10 units. Find the length of the altitude of the trapezoid.

**Problem 4: Find the area of an isosceles trapezoid if the length of the bases are 15 units and 9 units and length of the legs is 12 units.

**Problem 5: Calculate the perimeter of an isosceles trapezoid with the bases 20 units and 14 units and the length of the legs 10 units each.

**Problem 6: An isosceles trapezoid has a height of 7 units and the lengths of the two bases are 18 units and 10 units. Find the length of the non-parallel sides.

**Problem 7: If the area of an isosceles trapezoid is 225 square units with the one base 25 units and the height 15 units find the length of the other base.

**Problem 8: In an isosceles trapezoid the lengths of the two bases are 30 units and 22 units. If the height is 10 units find the length of the non-parallel sides.

**Problem 9: Given an isosceles trapezoid with the perimeter of 56 units and one of the bases measuring 16 units find the lengths of the other base and the legs.

**Problem 10: The height of an isosceles trapezoid is 12 units and length of the non-parallel sides is 15 units. If the length of one base is 24 units find the length of the other base.

Conclusion

The isosceles trapezoid is a unique geometric figure with the equal non-parallel sides which simplifies many of its properties and calculations. The Mastery of the formulas for the area height and side lengths is essential for the solving the various geometric problems involving the isosceles trapezoids. By applying these formulas and understanding their derivations one can efficiently tackle practical and theoretical problems in the geometry. The study of the isosceles trapezoids also reinforces broader concepts in the geometric analysis and problem-solving.