The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is described with a radius equal to half the length of the side of the triangle. Find the area of that part of the triangle which is not included in the circles (use π = 22/7 and √3 = 1.73).

Question

Accepted Answer

Let the side of the equilateral triangle be a = 28 cm.

Step 1: Area of the equilateral triangle:
Area = (√3 / 4) × a²
= (1.73 / 4) × (28)²
= (1.73 / 4) × 784
= 1.73 × 196
= 339.08 cm²

Step 2: Each circle has radius r = a/2 = 28/2 = 14 cm.
But only the part of the circle inside the triangle is considered. At each vertex, the circle covers a sector of 60° (since the angle at each vertex of an equilateral triangle is 60°).

Area of sector at one vertex = (60/360) × π × r²
= (1/6) × (22/7) × (14)²
= (1/6) × (22/7) × 196
= (1/6) × (22 × 28)
= (1/6) × 616
= 102.67 cm²

There are 3 such sectors (one at each vertex):
Total area covered by the sectors = 3 × 102.67 = 308.01 cm²

Step 3: Area of triangle not included in the circles = Area of triangle - Area covered by the 3 sectors
= 339.08 cm² - 308.01 cm²
= 31.07 cm²

Rounding to two decimal places, the answer is 31.08 cm².

Thus, the correct answer is 31.08 cm².

Answer

Answer

Answer