Can someone please help me! Big ideas number 22 8.4

26

Step-by-step explanation:

the whole area is the sum of the area of the rectangle in the middle and the 2 triangles on either side of the rectangle.

sBC = distance between (0,3) and (4,-1)

and that is the Pythagoras calculation with the coordinate differences

sBC² = (4-0)² + (-1 - 3)² = 16 + 16 = 32

sBC = sqrt(32) = sFE

to get the area of the rectangle we need also FB (or CE).

sFB² = (0 - -2)² + (3-1)² = 4 + 4 = 8

sFB = sqrt(8) = sCE

area of rectangle is

sBC×sFB = sqrt(32)×sqrt(8) = sqrt(32×8) = sqrt(256) = 16

the area of a right-angled triangle is

a×b/2

we have sFB and need sAF

sAF² = (-5 - -2)² + (4-1)² = 9 + 9 = 18

sAF = sqrt(18)

the area of the left triangle is

sFB×sAF/2 = sqrt(8)×sqrt(18)/2 = sqrt(8×18)/2 = sqrt(144)/2 = 12/2 = 6

for the right triangle we have sCE and need sED.

sED² = (2 - 4)² + (-3 - -5)² = 4 + 4 = 8

sED = sqrt(8)

the area of the right triangle is

sCE×sED/2 = sqrt(8)×sqrt(8)/2 = 8/2 = 4

so in total we have for the area

16 + 6 + 4 = 26

as a decimal x = -0.45

Step-by-step explanation:

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