. In mathematics, the Pythagorean Theorem, or Pythagoras's Theorem, is a fundamental relation in Euclidean geometry among the th
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This problem can be solved by calculating the area of the figure before removing the triangles, then subtracting the combined area of the triangles.
First, we have to find the area of the original composite figure. It appears that the figure consists of a 16 ft by 16 ft square with an 8 ft by 8 ft square cut out:
SA = (16*16) - (8*8)
SA = 256 - 64
SA = 192
The ORIGINAL area of this composite figure is 192 ft². Now we have to find the area of the removed triangles. Triangle area is found using half base times height. The base and height of each triangle appears to be 8, so we can plug in :
The area of each triangle is 32 ft². Finally, we should subtract the 3 triangles' area from the composite figure's area:
SA - 3(TA)
192 - 3(32)
192 - 96
96
The shaded region's area is 96 ft².
First, we have to find the area of the original composite figure. It appears that the figure consists of a 16 ft by 16 ft square with an 8 ft by 8 ft square cut out:
SA = (16*16) - (8*8)
SA = 256 - 64
SA = 192
The ORIGINAL area of this composite figure is 192 ft². Now we have to find the area of the removed triangles. Triangle area is found using half base times height. The base and height of each triangle appears to be 8, so we can plug in :
The area of each triangle is 32 ft². Finally, we should subtract the 3 triangles' area from the composite figure's area:
SA - 3(TA)
192 - 3(32)
192 - 96
96
The shaded region's area is 96 ft².