Questions on Geometry: Length, distance, coordinates, metric length answered by real tutors!

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Question 166152: Find the area of the polygon whose vertices are at (1,-4),(4,-1),(4,5),(-1,4)&(-2,-1).: Find the area of the polygon whose vertices are at (1,-4),(4,-1),(4,5),(-1,4)&(-2,-1).
Answer by Fombitz(1789) About Me  (Show Source):
You can put this solution on YOUR website!
First plot the points and see what you've got.
drawing( 300, 300, -6, 6, -6, 6,grid( 1 ),<BR> circle( 1, -4, .2 ),<BR> circle( 4, -1, .2 ),<BR> circle( 4, 5, .2 ),<BR> circle( -1, 4, .2 ),<BR> circle( -2, -1, .2 ),<BR> line(1,-4,4,-1),<BR> line(4,-1,4,5),<BR> line(4,5,-1,4),<BR> line(-1,4,-2,-1),<BR> line(-2,-1,1,-4),<BR> locate(1.1,-4.2,A),<BR> locate(4.1,-1.2,B),<BR> locate(4.2,5.2,C),<BR> locate(-1.5,4.2,D),<BR> locate(-2.5,-1.2,E)<BR> )
Define a couple of extra points that will help simplify the solution.
X at (4,4)
Y at (-1,-1)
drawing( 300, 300, -6, 6, -6, 6,grid( 1 ),<BR> circle( 1, -4, .2 ),<BR> circle( 4, -1, .2 ),<BR> circle( 4, 5, .2 ),<BR> circle( -1, 4, .2 ),<BR> circle( -2, -1, .2 ),<BR> circle(4,4,.2),<BR> circle(-1,-1,.2),<BR> green(line(4,4,-1,4)),<BR> green(line(-2,-1,4,-1)),<BR> green(line(-1,-1,-1,4)),<BR> green(line(4,-1,4,4)),<BR> locate(-1.2,-1.2,Y),<BR> locate(4.2,4,X),<BR> line(1,-4,4,-1),<BR> line(4,4,4,5),<BR> line(4,5,-1,4),<BR> line(-1,4,-2,-1),<BR> line(-2,-1,1,-4),<BR> locate(1.1,-4.2,A),<BR> locate(4.1,-1.2,B),<BR> locate(4.2,5.2,C),<BR> locate(-1.5,4.2,D),<BR> locate(-2.5,-1.2,E)<BR> )
Now we can find the areas of the individual triangles and square and add them together.
Area of a square is s*s where s is the side length.
Area of a triagle is half the product of base and height.
.
.
.
Square BXDY : A=s^2=5^2=25
Triangle XCD :A=(1/2)bh=(1/2)(5)(1)=5/2
Triangle DEY :A=(1/2)bh=(1/2)(1)(5)=5/2
Triangle EAB :A=(1/2)bh=(1/2)(6)(3)=9
Now add all of the areas,
A[p]=25+5/2+5/2+9
A[p]=39