The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the part of the triangle that is not included in the circles (use $\pi = \frac{22}{7}$ and \(\sqrt{3} = 1.7

Question

The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the part of the triangle that is not included in the circles (use $\pi = \frac{22}{7}$ and $\sqrt{3} = 1.73$).

Accepted Answer

31.08 cm². The area of the equilateral triangle is $\frac{\sqrt{3}}{4}a^2$. The three inside parts are 60° sectors of radius 14 cm, whose total area is $3\times \frac{60}{360}\pi(14)^2$. Subtracting gives the required uncovered area.

The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the part of the triangle that is not included in the circles (use \(\pi = \frac{22}{7}\) and \(\sqrt{3} = 1.73\)).

Solution

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