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Ask iit jee aieee pet cbse icse state board experts Expert Question: Find the area of pentagon with vertices A(1,1),B(7,21),C(7,-3),D(12,2) and E(0,-3) as a su
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raza123 (0)

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Find the area of pentagon with vertices A(1,1),B(7,21),C(7,-3),D(12,2) and E(0,-3) as a su
    
allamraju (3410)

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Is the ans 113/2 sq.units.I will explain if i am correct.

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edison (4435)

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That is simple.
As coordinates of all 5 vertices of pentagon are given thus we can divide the pentagon into 3 triangles.

Thus area of pentagon = Sum of area of the three triangles

The most incomprehensible thing about the world is that it is

at all comprehensible.
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edison (4435)

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The (signed) area of a planar triangle specified by its vertices v_i=(x_i,y_i) for i=1, 2, 3 is given by


















Delta = 1/(2!)|x_1 y_1 1; x_2 y_2 1; x_3 y_3 1|
(1)

= 1/2(-x_2y_1+x_3y_1+x_1y_2-x_3y_2-x_1y_3+x_2y_3).
(2)



The most incomprehensible thing about the world is that it is

at all comprehensible.
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