source : yahoo.com

## Find the area of the following shape. You must show all work to receive credit.?

There are two ways you could do this:

define the other three corners for the surrounding square: X(3,-8), Y(3,0), Z(-5,0)

area of excluded triangles:

(C,X,B) area: 3

(C,D,Y) area: 5

(D,E,Z) area: 9

(A,E,F) area: 5

total = 22

area of shape = 64 – 22 = 42

or you could divide your shape into triangles and add up their areas:

(A,B,F) area: 6

(B,C,F) area: 8

(C,D,F) area: 16

(D,E,F) area: 12

total area of shape = 42

Here are the calculations for the eight triangles:

– – – – – –

(3,-5,,C)(3,-8,,X)(1,-8,,B): Vertices: (3,-5) (3,-8) (1,-8)

sides (c,x,b): 2, 3.6056, 3

angles (C,X,B): 33.6901°, 90°, 56.3099° is a right scalene triangle

area: 0.5*sin(A)*b*c=3 perimeter: 8.6056

– – – – – –

(3,-5,,C)(1,0,,D)(3,0,,Y): Vertices: (3,-5) (1,0) (3,0)

sides (c,d,y): 2, 5, 5.3852

angles (C,D,Y): 21.8014°, 68.1986°, 90° is a right scalene triangle

area: 0.5*sin(A)*b*c=5 perimeter: 12.3852

– – – – – –

(1,0,,D)(-5,-3,,E)(-5,0,,Z): Vertices: (1,0) (-5,-3) (-5,0)

sides (d,e,z): 3, 6, 6.7082

angles (D,E,Z): 26.5651°, 63.4349°, 90° is a right scalene triangle

area: 0.5*sin(A)*b*c=9 perimeter: 15.7082

– – – – – –

(-5,-8,,A)(-5,-3,,E)(-3,-6,,F): Vertices: (-5,-8) (-5,-3) (-3,-6)

sides (a,e,f): 3.6056, 2.8284, 5

angles (A,E,F): 45°, 33.6901°, 101.3099° is an obtuse scalene triangle

area: 0.5*sin(A)*b*c=5 perimeter: 11.434

– – – – – –

(-5,-8,,A)(1,-8,,B)(-3,-6,,F): Vertices: (-5,-8) (1,-8) (-3,-6)

sides (a,b,f): 4.4721, 2.8284, 6

angles (A,B,F): 45°, 26.5651°, 108.4349° is an obtuse scalene triangle

area: 0.5*sin(A)*b*c=6 perimeter: 13.3006

– – – – – –

(1,-8,,B)(3,-5,,C)(-3,-6,,F): Vertices: (1,-8) (3,-5) (-3,-6)

sides (b,c,f): 6.0828, 4.4721, 3.6056

angles (B,C,F): 97.125°, 46.8476°, 36.0274° is an obtuse scalene triangle

area: 0.5*sin(A)*b*c=8 perimeter: 14.1604

– – – – – –

(3,-5,,C)(1,0,,D)(-3,-6,,F): Vertices: (3,-5) (1,0) (-3,-6)

sides (c,d,f): 7.2111, 6.0828, 5.3852

angles (C,D,F): 77.6609°, 55.4915°, 46.8476° is an acute scalene triangle

area: 0.5*sin(A)*b*c=16 perimeter: 18.679

– – – – – –

(1,0,,D)(-5,-3,,E)(-3,-6,,F): Vertices: (1,0) (-5,-3) (-3,-6)

sides (d,e,f): 3.6056, 7.2111, 6.7082

angles (D,E,F): 29.7449°, 82.875°, 67.3801° is an acute scalene triangle

area: 0.5*sin(A)*b*c=12 perimeter: 17.5249

– – – – – –

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