Isosceles Trapezoid Formula

What is Isosceles Trapezoid?

An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one set of opposite sides in Euclidean geometry. It is a trapezoid in its most extreme form. Isosceles trapezium shape can also be described as a trapezoid with the same measurement for both legs and base angles. Two opposite sides of an isosceles trapezoid are parallel, while the other two sides are of equal length. In addition, the diagonals are of the same length. An isosceles trapezoid's base angles are equal in size.


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Area of Isosceles Trapezium

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.

The average of the base and top (parallel sides) lengths times the height equals the area of isosceles trapezium. If we write AD = a and BC = b in the trapezium diagram shown below, and the height h is the length of a perpendicular line segment between AD and BC.


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Then the area of isosceles trapezium formula is as follows:

Area of isosceles trapezoid, \[A=\frac{h}{2}(a+b))\]


How to find the Perimeter of an Isosceles Trapezoid?

A perimeter is a path or length that encompasses/surrounds/outlines a shape. The perimeter can be calculated in a variety of ways. The length of fencing necessary to encircle a yard or garden is known as the calculated perimeter.

In the diagram given below if we write AD = a and BC = b, AB = CD = c in the trapezium diagram.


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Then the perimeter of isosceles trapezium is given as follows:

Perimeter of isosceles trapezium, P = a + b + 2c


Problems on Isosceles Trapezoid Formula

1. If the length of two parallel sides of the isosceles trapezoid is 8 cm and 5 cm respectively. The height of the perpendicular line segment between the two parallel sides is 7cm. Calculate the area of isosceles trapezium.

Ans: Here a = 8 cm, b = 5 cm and h = 7 cm. 

The area of isosceles trapezium formula is as follows:

Area of isosceles trapezoid, \[A=\frac{h}{2}(a+b)\]

Now substituting the values in the formula we get

Area of isosceles trapezoid, \[A=\frac{7}{2}(8+5)\]

A=72(13)

A = 45.5 cm2.

Therefore the area of isosceles trapezium is 45.5 cm2.


2. Calculate the perimeter of isosceles trapezium if the length of two parallel sides is 10 cm and 7 cm and the length of the leg is 8 cm. 

Ans: Here a = 10 cm, b = 7 cm and c = 8 cm.

The perimeter of isosceles trapezium is given as follows:

Perimeter of isosceles trapezium, P = a + b + 2c

Substituting the values we get

P = 10 + 7 + 2 × 8

P = 10 + 7 + 16

P = 33 cm.

Therefore the perimeter of isosceles trapezium is 33 cm.


3. The area of the isosceles trapezium is 54 cm2 and the length of two parallel sides of the isosceles trapezoid is 10 cm and 8 cm respectively. Find the height of the perpendicular line segment between the two parallel sides.

Ans: Here the area of the isosceles trapezium A = 54 cm2, a = 10 cm and b = 8 cm.

To find the height of the perpendicular line segment between the two parallel sides we will use the area of isosceles trapezium formula.

Area of isosceles trapezoid, \[A=\frac{h}{2}(a+b)\]

Substituting the values we get

54 = h/2(10 + 8)

54 = h/2(18)

54/18 = h/2

h = 6 cm.

Therefore the height of the perpendicular line segment between the two parallel sides is 6 cm.


Conclusion

The number of sides in an isosceles trapezoid is four. The two opposing sides (bases) are parallel to each other, whereas the remaining two sides are equal in length but not parallel. Two crucial and fundamental mathematical concepts are perimeter and area. Perimeter and area calculation aid in the quantification of physical space as well as laying the groundwork for more complex mathematics such as algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape, while area indicates how much surface area the shape covers. People like architects, engineers, and graphic designers use area and perimeter knowledge on a daily basis, and it is a type of mathematics that is very useful to the common public.

FAQs (Frequently Asked Questions)

1. What is a Isosceles Trapezoid?

Ans: An isosceles trapezoid is a trapezoid with non-parallel sides and base angles that have the same length. In other terms, an isosceles trapezoid has two opposite sides (bases) that are parallel and two non-parallel sides that are of equal length.

2. What is the Area of Isosceles Trapezium?

Ans: The area of isosceles trapezium formula is 

A = h/2(a + b)

3. What is the Perimeter of Isosceles Trapezium?

Ans: The perimeter of isosceles trapezium is,

P = a + b + 2c