What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m

Given:

height = 6m

chord = 20 m

We need to find the radius of the circle.

20 m = 2 √ [ 6m (2 x radius - 6 m) ]

20 m / 2 = 2 √ [ 6m (2 x radius - 6 m) ] / 2

10 m = √ [ 6m (2 x radius - 6 m) ]

(10 m) ² = √[ 6m (2 x radius - 6 m) ] ²

100 m² = 6 m (2 x radius - 6 m)

100 m² = 12 m x radius - 36 sq m

100 m² + 36 m² = 12 m x radius - 36 m² + 36 m²

136 m² = 12 m x radius

136 m² / 12 m = 12 m x radius / 12 m

11.333 m = radius

the area beneath an arc:

Area = r ² x arc cosine [ (r - h) / r ] - (r - h) x √ (2 x r x h - h ²).

r ² = (11.333 m) ² = 128.444 m ²

r - h = 11.333 m - 6 m = 5.333 m

r * h = 11.333 m x 6 m = 68 m ²

Area = 128.444 m ² x arc cosine [ 5.333 m / 11.333 m ] - 5.333 m x √ [ 2 x 68 m ² - 36 m ² ]

Area = 128.444 m ² x arc cosine [ 0.4706 ] - 5.333 m x √ [ 100m ² ]

Area = 128.444 m ² x 1.0808 radians - 5.333 m x 10 m

Area = 138.828 m ² - 53.333 m ²

Area = 85.4 m ²