The figure shows a square with 16 circles. Find the area of the shaded region if the side of the square is 56 cm.
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The figure shows a square with 16 circles.
we have to find the area of the shaded region of the side of the square is 56 cm.
Solution : from figure,
4 × diameter of each circle = edge length of square
⇒4 × 2r = 56 cm
⇒r = 7 cm
area of shaded region = area of square - 16 × area of each circle.
= (edge length)² - 16 × πr²
= (56 cm)² - 16 × 22/7 × 7cm × 7cm
= 3136 cm² - 16 × 22 × 7 cm²
= 3136 cm² - 2464 cm²
= 672 cm²
Therefore the shaded region of square is 672 cm².
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