Answer:
Area = 85.4 m^2
Explanation:
Given data:
height h = 6 m
length l = 20 m
we know that chord length is given as
\(chord = 2 \sqrt{ [ height x ( 2 x radius - height) ]}\)
\(20 m= 2 \sqrt{ [ 6 m x ( 2 x radius - 6 m ) ]}\)
solviing for radius r we get
r = 11.33 m
we know that area of segment of circle is given as
\(Area =r^2 \times arc cosine [ \frac{r-h}{r}] - (r-h) \times \sqrt{(2\times r\times h - h^2)}\)
r - h = 11.33 - 6 = 5.33m
\(r^2 = 11.33^2 = 128.44 m^2\)
r -h = 11.33 - 6 = 68 m^2
\(Area = 128.44 \times arc cosine [\frac{5.33}{11.33}] - 5.33 \times \sqrt{2\times 68 - 36 }\)
Area = 85.4 m^2
