Question

If ABCD is a square, and the area covered by the blue equilateral triangle is 49√3 cm2, what will be the area covered by the yellow region (in cm2)?

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Answer 1

The area covered by the yellow region is 42 cm².

If ABCD is a square, and the area covered by the blue equilateral triangle is 49√3 cm².

We have to find the area covered by the yellow region (in cm²).

Let radius of of each circle is r.

∴ the edge length of square = edge length of equilateral triangle = 2r

Here, area of equilateral triangle = √3/4 × side length²

⇒49√3 = √3/4 × (2r)²

⇒r = 7

now edge length of square = 2 × 7 = 14 cm

∴ Area covered by yellow region = area of square - 2 × area of a semi circle

= (14)² - 2 × 1/2 × π × 7²

= 196 - 22/7 × 7 × 7

= 196 - 154

= 42 cm²

Therefore the area covered by the yellow region is 42 cm².