A quadrilateral is inscribed in a circle, the sides of which are alternately equal to 4, 6, 8, and 12 cm.

univerkov | June 19, 2021 | education

A quadrilateral is inscribed in a circle, the sides of which are alternately equal to 4, 6, 8, and 12 cm. Find the area of the quadrilateral.

The area of a quadrilateral inscribed in a circle is equal to the square root of the product of the difference of the quadrilateral semiperimeter and the lengths of its sides.

Let’s define the semi-perimeter of the quadrangle: p = (AB + BC + CD + AD) / 2 = (64 + 8 + 12 + 4) / 2 = 30/2 = 15 cm.

Savsd = √ (p – AB) * (p – BC) * (p – CD) * (p – AD) = √9 * 7 * 3 * 11 = 3 * √231 cm2.

Answer: The area of the quadrangle is 3 * √231 cm2.

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