Answer:
26
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