If A(−7,5),B(−6,−7),C(−3,−8) and D(2,3) are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.

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Filo · Accepted Answer

Given: ABCD is a quadrilateral whose vertices are A(−7,50,B(−6,−7),C(−3,−8) and D(2,3).By joining AC, we get two triangles ABC and ADCWe know that:Area of ΔABC=21​[x1​(y2​−y3​)+x2​(y3​−y1​)+x3​(y1​−y2​)]Area of triangle ABC:=21​[−7(−7−(−8)]+(−6)[(−8)−5]+(−3)[5−(−7)]=21​[−7×(1)+(−6)×(−13)+(−3)×12]=21​[−7+78−36]=21​×35=235​ sq. units.Area of triangle ADC.=21​[−7(−8−3)+(−3)(3−5)+(2)(−5(−8)]=21​[(−7)×(−11)+(−3)×(−2)+2×13]=21​[77+6+26]=2109​ sq. units.Now, Area of quadrilateral PQRS=Area of triangle ABC+Area of triangle ADC=35/2+109/2=72 sq. units.

Question Text	If $A (- 7, 5), B (- 6, - 7), C (- 3, - 8)$ and $D (2, 3)$ are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.
Answer Type	Text solution:1
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If $A (- 7, 5), B (- 6, - 7), C (- 3, - 8)$ and $D (2, 3)$ are the vertices of a quadrilateral ABCD then find the area of the quadrilateral.

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