What is the area of this figure? enter your answer in the box. units² an irregular heptagon is graphed on a coordinate plane. the horizontal x-axis ranges from negative 6 to 6 in increments of 1. the vertical y-axis ranges from negative 6 to 6 in increments of 1. the vertices of the heptagon are located at begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair negative 4 comma 5 end ordered pair, begin ordered pair negative 2 comma 3 end ordered pair, begin ordered pair 3 comma 4 end ordered pair, begin ordered pair 4 comma 3 end ordered pair, begin ordered pair 4 comma negative 3 end ordered pair, and begin ordered pair negative 3 comma negative 3 end ordered pair.

area of the given heptagon is 54 square units.

It is a polygon having 7 sides.

coordinates  of all 7 vertices are given as:

(-5,3)

(-4,5)

(-2,3)

(3,4)

(4,3)

(4,-3)

(-3,-3)

in the uploaded diagram. heptagon has been split into 5 triangles, called T1, T2, T3, T4, and T5.

Now the area of the heptagon= T1+T2+T3+T4+T5

AreaT1= 3*2/2=3

AreaT2= 3*6/2=9

AreaT5=6*7/2=21

AreaT3=14.5, Using the coordinate formula for the area of a triangle.

AreaT4=6.5,  Using the coordinate formula for the area of a triangle.

Total Area= 3+9+21+14.5+6.5= 54

hence, the area of the given heptagon is 54 square units.

to get more about polygon refer to the link,

link

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