What is the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? Round your answer to the nearest whole number. A. 85.4 m2 B. 74.6 m2 C. 8.54 m2 D. 746.67 m2

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