2 added 44 characters in body
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A more geometrical approach based on CP3D surface-surface intersections boundary style...

inter = ContourPlot3D[{h == 0, g == 0}, {x, -4, 4}, {y, -4, 4}, {t, -4, 4}, Mesh -> None, ContourStyle -> Directive[Orange, Opacity[0.3], Specularity[White, 30]], BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Blue}]

reg = DiscretizeGraphics[inter, Line]

RegionMeasure[reg]

(* 10.9518 *)

inter = ContourPlot3D[{h == 0, g == 0}, {x, -4, 4}, {y, -4, 
   4}, {t, -4, 4}, Mesh -> None, 
  ContourStyle -> 
   Directive[Orange, Opacity[0.3], Specularity[White, 30]], 
  BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Blue}]

reg = DiscretizeGraphics[inter, Line]

RegionMeasure[reg]

(* 10.9518 *)

A more geometrical approach based on CP3D surface-surface intersections boundary style...

inter = ContourPlot3D[{h == 0, g == 0}, {x, -4, 4}, {y, -4, 4}, {t, -4, 4}, Mesh -> None, ContourStyle -> Directive[Orange, Opacity[0.3], Specularity[White, 30]], BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Blue}]

reg = DiscretizeGraphics[inter, Line]

RegionMeasure[reg]

(* 10.9518 *)

A more geometrical approach based on CP3D surface-surface intersections boundary style...

inter = ContourPlot3D[{h == 0, g == 0}, {x, -4, 4}, {y, -4, 
   4}, {t, -4, 4}, Mesh -> None, 
  ContourStyle -> 
   Directive[Orange, Opacity[0.3], Specularity[White, 30]], 
  BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Blue}]

reg = DiscretizeGraphics[inter, Line]

RegionMeasure[reg]

(* 10.9518 *)
1
source | link

A more geometrical approach based on CP3D surface-surface intersections boundary style...

inter = ContourPlot3D[{h == 0, g == 0}, {x, -4, 4}, {y, -4, 4}, {t, -4, 4}, Mesh -> None, ContourStyle -> Directive[Orange, Opacity[0.3], Specularity[White, 30]], BoundaryStyle -> {1 -> None, 2 -> None, {1, 2} -> Blue}]

reg = DiscretizeGraphics[inter, Line]

RegionMeasure[reg]

(* 10.9518 *)