The answer is "85.4 m²".
To find the area, first we have to find the radius;and given that height = 6mchord = 20 mNow,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
Thus radius is 11.333m.
t.To find the area beneath an arc:
Area = r² x arc cosine [ ( r - h ) / r ] - ( r - h ) x √( 2 x r x h - h² ).
r² = (11.333 m)² = 128.444 m² r - h= 11.333 m - 6 m = 5.333 m r * h = 11.333 m x 6 m = 68 m²
Area = 128.444 m² x arc cosine [ 5.333 m / 11.333 m ] - 5.333 m x √[ 2 x 68 m² - 36 m² ]
Area = 128.444 m² x arc cosine [ 0.4706 ] - 5.333 m x √ [ 100m² ]
Area = 128.444 m² x 1.0808 radians - 5.333 m x 10 m
Area = 138.828 m² - 53.333 m²
Area = 85.4 m²