Question

the area of an equilateral triangle is 49√3cm^2. taking each angular point as centre,a circle is described with radius equal to half the length of the side of the triangle as shown in the figure.find the area of the position in the triangle not included in the circles.

Answer 1

Given,area of equilateral triangle = 49 root 3 cm square.
From diagram radius = 7cm
theta = 60 degrees.
Area of 3 sectors = 3 (theta/ 360 × pi r square)
= 3 (60/360×22/7×7×7)
=11×7
=77cm square.
Therefore not included area = 49 root 3 - 77
= 49×1.732-77
= 84.8729- 77
= 7.8729 cm square..
Hope Helpful..

Answer 2

Answer:

area of equilateral triangle,=

$49 \sqrt{3}$

49 root 3 cm2 =root3/4 *a2

=14 cm

area of sector = 60/360*22/7*7*7

= 1/6*22*7

=1/3*11*7

=77/3

AS THERE ARE THREE SECTOR ,

HENCE MULTIPLY BY THREE

= 77/3*3

=77 CM2

NOW.,

AREA OF TRIANGLE NOT INCLUDED =

AREA OF EQUILATERAL TRIANGLE -AREA OF SECTOR

=49root3-77

=49*1.7-77

=88.77-77

=7.77 cm2