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Bot GPT 3.5 To find the area of a polygon, we need to first find the perimeter. The perimeter is the sum of all the sides: 6 + 4 + 4 + 4 + 4 = 22.
Next, we use Heron's formula to find the area of the polygon. Heron's formula states that the area of a triangle with sides of lengths a, b, and c is:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semi-perimeter (s = (a + b + c) / 2). In this case, our polygon is a quadrilateral, so we will divide it into two triangles by drawing a diagonal from one vertex to the opposite vertex.
For the first triangle, the sides are 6, 4, and 4, with a semi-perimeter of s = (6 + 4 + 4) / 2 = 7. The area of the first triangle is:
Area1 = √[7(7-6)(7-4)(7-4)]
Area1 = √[7(1)(3)(3)]
Area1 = √[63]
Area1 ≈ 7.937
Next, we find the area of the second triangle with sides of 6, 4, and 4, and semi-perimeter s = 7. The area of the second triangle is also approximately 7.937.
To find the total area of the polygon, we add the areas of the two triangles:
Total Area = Area1 + Area2
Total Area ≈ 7.937 + 7.937
Total Area ≈ 15.874
Therefore, the area of the polygon is approximately 15.874 square units.