The answer is: "approximately 62 m² " .
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Explanation:
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We find the dimensions ("L * w") ; which are length and width, respectively; to find the area of the entire rectangle (assuming that "shaded" or "non-shaded" regions are irrelevant).
The area of the rectangle, "A = L * w" ;
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If EACH of the circles has a Circumference, "C = 37.7 m" ; we need to find the diameter, "d", of one of the circles, and multiply that value by "2" ; to get the length, "L" , of the rectangle.
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Note: C = π * d ;
Use "3.14" as an approximation for "π"; to find the diameter, "d" .
Since; "C = π * d " ;
Rearrange the equation to isolate "d" on one side of the equation; then plug in our known values to solve for "d" ;
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→ C = π * d ;
Divide each side of the equation by "π"; to isolate "d" on one side of the equation ;
→ C / π = (π * d) / π ;
to get: C / π = d ; ↔ d = C / π ;
→ d = C / π = (37.7 m) / (3.14) ;
to get:
→ d = 12.0063694267515924 m
Now, the length of the rectangle, "L = 2*d = 2 * 12 m = 24 m ;
The width of the rectangle, "w" = "d" = 12 m ;
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The total area of the rectangle (regardless shade or unshaded regions):
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A = L * w = 24 m * 12 m = (24 * 12) m² = 288 m² .
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Now, we find the area of one of the circles; multiply that value by "2" ; {since there are two identical-area circles.}.
{Note that the circles within the rectangle are "unshaded".}.
Then subtract this "total value (area)" ; from "288 m² " (the total area of the triangle) ; and we are left with the area of the shaded regions.
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So; The area of one circle:
→ " A = π r² " ; in which: A = area of the circle ;
π = 3.14 (approximation);
r = length of radius ;
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The radius, "r" , equals "1/2" the length of the diameter, "d" ;
So; " r = d / 2 = (12 m / 2) = 6 m " ;
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→ A = π r²
→ A = (3.14) * (6 m)² ;
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→ {Note: " (6 m)² = 6m * 6m = 36 m² . " }.
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→ A = (3.14) * (6 m)² ;
= (3.14) * (36 m²) ;
= [ (3.14) * (36) ] m² ;
= 113.04 m² ;
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Now, since there are 2 (TWO) circles of equal area ;
multiply this value by "2" ;
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→ 2 * (113.04 m²) = 226.08 m² ; round to 226 m² ;
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→ Now, subtract this value, FROM the value of the TOTAL AREA of this rectangle, to get our answer — "the area of the shaded region of the rectangle / figure" .
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→ 288 m² − 226 m² = 62 m² .
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→ The answer is: " approximately 62 m² " .
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