are of an irregular hexagon with 12 m side b and 8 m side a

1 answer

To find the area of an irregular hexagon with side lengths 12 m and 8 m, you can divide the hexagon into smaller triangles and then calculate the area of each triangle separately.

First, divide the hexagon into 4 triangles by drawing a diagonal from one corner to the opposite corner.

Each triangle will have two sides of length 12 m (side b) and one side of length 8 m (side a).

Using Heron's formula to calculate the area of each triangle, you'll need to find the semi-perimeter (s) first:

s = (12 + 12 + 8) / 2 = 16

Then, you can calculate the area of each triangle using the formula:

Area of a triangle = √(s * (s - a) * (s - b) * (s - c))

where a, b, and c are the sides of the triangle.

Triangle 1:
Area = √(16 * (16 - 8) * (16 - 12) * (16 - 12))
= √(16 * 8 * 4 * 4)
= √(2048)
≈ 45.25 m²

Triangle 2, 3, and 4:
Since all the triangles have the same sides, their areas will be the same as Triangle 1, which is approximately 45.25 m².

Finally, the total area of the irregular hexagon will be the sum of the areas of the 4 triangles:

Total Area = 45.25 m² + 45.25 m² + 45.25 m² + 45.25 m²
= 181 m²

Therefore, the area of the irregular hexagon is approximately 181 square meters.