Question
In a quadrilateral ABCD, the diagonals AC and BD
intersect at O. If AO = 8 cm, OC = 12 cm, BO = 6 cm, and OD = 9 cm, find the area of the quadrilateral using the formula for the area of a cyclic quadrilateral.Solution
To find the area of quadrilateral ABCD where diagonals AC and BD intersect at O, and the quadrilateral is cyclic or the diagonals are perpendicular, use the formula:
Compute the diagonals:
Substitute into the formula:
The area of the quadrilateral is 150 cm².
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