in quadrilateral ABCD BC is the diagonal BD is perpendicular to BC and c x is perpendicular to ab if a b equal to 25 CM BC equal to 16 cm 6 CX equal to 8 cm and BC equal to 5 cm find the area of the quadrilateral
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cca
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Let O be the point in the middle where the diagonals cross and let the distances from the corners to the middle be p = AO, q = BO, r = CO, s = DO.
Now each triangle AOB forms a right angle so AB² = p² + q², BC² = q²+r², CD² = r²+s², DA²=s²+p². Adding the squares of opposite edges gives
AB² + CD² = p² + q²+r²+s² = BC²+DA².
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