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Question

If A(0,0),B(12,0),C(12,2),D(6,7) and E(0,5) are the vertices of the pentagon ABCDE, then its area (in sq units) is


A

58

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B

60

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C

61

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D

62

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E

63

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Solution

The correct option is E

63


Explanation for the correct option:

Finding the area:

Let (x1,y1)=(0,0),(x2,y2)=(12,0),(x3,y3)=(12,2),(x4,y4)=(6,7),(x5,y5)=(0,5)

The area of pentagon =½[(x1y2+x2y3+x3y4+x4y5+x5y1(y1x2+y2x3+y3x4+y4x5+y5x1)

Now, substitute the values, we get

=(½)[0(0)+12(2)+12(7)+6(5)+0(0)-0+0+2(6)+7(0)+5(0)]=(½)(24+84+30-12)=63

Therefore, the correct option is option E.


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