# {Calculator} Area of Isosceles Trapezoid with Inscribed Circle

## area of isosceles trapezoid with inscribed circle calculator based on user input

An isosceles trapezoid is a quadrilateral with two sides that are equal in length and two other sides that are not. The equal sides are called the bases of the trapezoid, and the other two sides are called the legs. The bases are always parallel to each other, and the legs are always perpendicular to the bases.

An inscribed circle is a circle that is completely inside the trapezoid and touches all four sides of the trapezoid at points called the tangency points. The diameter of the inscribed circle is always equal to the distance between the two bases of the trapezoid.

The area of an isosceles trapezoid with an inscribed circle can be calculated by first finding the area of the trapezoid and then adding the area of the circle. The formula for the area of a trapezoid is:

Area = (side1 + side2) * height / 2

Where "side1" and "side2" are the lengths of the bases of the trapezoid, and "height" is the distance between the bases, perpendicular to them.

To find the area of the inscribed circle, you can use the formula for the area of a circle:

Where "π" is the mathematical constant pi, approximately equal to 3.14, and "radius" is the radius of the circle. The radius of the inscribed circle is equal to half the diameter, which is equal to half the distance between the bases of the trapezoid.

To find the total area of an isosceles trapezoid with an inscribed circle, you can add the area of the trapezoid and the area of the circle:

Total Area = Area of trapezoid + Area of circle
= (side1 + side2) * height / 2 + π * radius^2

This formula can be used to calculate the area of any isosceles trapezoid with an inscribed circle, as long as you know the lengths of the bases and the height of the trapezoid.

It is important to note that the units of measurement for the sides and height of the trapezoid must be the same. If the sides are measured in inches and the height is measured in feet, for example, you will need to convert one of the measurements to the same unit as the other before you can use the formula.

In addition, the radius of the inscribed circle is always measured in the same unit as the sides and height of the trapezoid. If the sides and height are measured in inches, for example, the radius of the inscribed circle will also be measured in inches.

Knowing the area of an isosceles trapezoid with an inscribed circle can be useful in a variety of situations. For example, you might use it to calculate the amount of paint or other material needed to cover a surface shaped like an isosceles trapezoid with an inscribed circle. Or, you might use it to determine the size of a piece of fabric or other material needed to cover an object shaped like an isosceles trapezoid with an inscribed circle.

Regardless of how you use it, the formula for calculating the area of an isosceles trapezoid with an inscribed circle is a valuable tool to have in your mathematical toolkit. So, it is a good idea to memorize it and practice using it to become proficient in calculating the area of isosceles trapezoids with inscribed circles.