A quadrilateral with sides (sequentially) 7 cm, 24 cm, 20 cm, 15 cm is inscribed in a circle. Find the area of the quadrilateral.

univerkov | February 21, 2021 | education

The area of a quadrilateral inscribed in a circle can be calculated by the formula S = √ (p – a) (p – b) (p – c) (p – d), where p is the semiperimeter of the quadrilateral, a, b, c and d are the sides.

p = (7 + 24 + 20 + 15) / 2 = 66/2 = 33.

S = √ (33 – 7) (33 – 24) (33 – 20) (33 – 15) = √ (26 * 9 * 13 * 18) = √ (2 * 13 * 9 * 13 * 2 * 9) = 2 * 13 * 9 = 234 cm².

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