Question

An equilateral triangle has each side 2m. With all three corners as centers circles are described each of radius one meter. Find the area of the remaining portion of the triangle

Answer 1

hea mate here is the answer

Answer 2

Answer:

The figure will look like the one shown in the picture.

Area of the remaining portion of the triangle = Total area of the triangle - total area occupied by the three circles in the triangle

We already know that area of an equilateral triangle is √3/4 (side)².

Hence, the area of the triangle is √3/4 * (2)² = √3..................................(1)

Now, the the formula for the area of one part of the circle is (Ф/360°) * π r², where Ф  is the angle subtended by the arc at the center of the circle.

Further, we know that each angle subtended by the equilateral angled triangle is 60°.

Therefore, area  = ( 60/360) * π (1)² = π/6

Therefore, area of 3 such circular areas = 3 * ( π/6)  = π/2.........................(2)

Now, the value of π = 3.14

Therefore, π/2 = 1.57...................................(3)

Now, the remaining area  = Area of the triangle - area occupied by parts of the three circles

Therefore, remaining area =  √3 - 1.57 = 1.732 - 1.57 = 0.162 m².

Therefore the answer is 0.162 m².