Find the area of an isosceles trapezoid circumscribed about a circle if its bases are 2 cm and 8 cm.

It is known from the condition that an isosceles trapezoid, circumscribed about a circle, with base lengths of 2 cm and 8 cm. Find the area of ​​the trapezoid.

Let’s start by remembering that a trapezoid can only be inscribed in a circle that is isosceles. Based on this, we can write the equality of opposite sides as:

2 + 8 = 2x, where x is the side of the trapezoid.

2x = 10;

x = 5 cm side.

Let us find the length of the height lowered to a greater base using the Pythagorean theorem:

BH = √ (5 ^ 2 – ((8 – 2) / 2) ^ 2) = √ (25 – 9) = 4 cm.

The area of ​​the trapezoid is equal to the product of half the sum of the bases by the height:

S = (a + b) / 2 * h = (2 + 8) / 2 * 4 = 20 sq. units.