find the area of the polygon an E shape with the numbers 10 10 10 10 4 4 4 16 16 22 5 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.