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find the area of the polygon an E shape with the numbers 10 10 10 10 4 4 4 16 16 22 5 5
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GPT 3.5
To find the area of the polygon, we can split it into two separate triangles:
1) Triangle with sides 10, 10, and 16
2) Triangle with sides 4, 5, and 22
Using Heron's formula to find the area of each triangle:
1) For the first triangle with sides 10, 10, and 16:
s = (10 + 10 + 16)/2 = 18
Area = √(18(18-10)(18-10)(18-16)) = √(18*8*8*2) = √(2304) = 48
2) For the second triangle with sides 4, 5, and 22:
s = (4 + 5 + 22)/2 = 15.5
Area = √(15.5(15.5-4)(15.5-5)(15.5-22)) = √(15.5*11.5*10.5*7.5) ≈ √(1962) ≈ 44.3
Adding the areas of both triangles:
Total Area = 48 + 44.3 = 92.3
Therefore, the area of the polygon is approximately 92.3.
1) Triangle with sides 10, 10, and 16
2) Triangle with sides 4, 5, and 22
Using Heron's formula to find the area of each triangle:
1) For the first triangle with sides 10, 10, and 16:
s = (10 + 10 + 16)/2 = 18
Area = √(18(18-10)(18-10)(18-16)) = √(18*8*8*2) = √(2304) = 48
2) For the second triangle with sides 4, 5, and 22:
s = (4 + 5 + 22)/2 = 15.5
Area = √(15.5(15.5-4)(15.5-5)(15.5-22)) = √(15.5*11.5*10.5*7.5) ≈ √(1962) ≈ 44.3
Adding the areas of both triangles:
Total Area = 48 + 44.3 = 92.3
Therefore, the area of the polygon is approximately 92.3.