Find the area of the shaded portion in the equilateral triangle with sides 6.
1 answer:
We know that
area of equilateral triangle=s²*√3/4
in this problem
s=6 units
area of equilateral triangle=6²*√3/4-----> 9√3 units²
<span>the internal angles of an equilateral triangle are equal to 60 degrees
</span>
area of a circle=pi*r²
for a circle with radius r=3 units
area=pi*3²-----> 9*pi units²
see the attached figure to better understand the problem
the area of the figure ABC is equal to the area of the circle divided by 6
Area figure ABC=9*pi/6-----> (3/2)*pi units²
<span>the area of the shaded portion is equal to
</span>[area of equilateral triangle-3*area figure ABC]
9√3 units²-3*(3/2)*pi units²-----> 9√3 units²-(9/2)*pi units²
the answer is
9√3 units²-(9/2)*pi units²
area of equilateral triangle=s²*√3/4
in this problem
s=6 units
area of equilateral triangle=6²*√3/4-----> 9√3 units²
<span>the internal angles of an equilateral triangle are equal to 60 degrees
</span>
area of a circle=pi*r²
for a circle with radius r=3 units
area=pi*3²-----> 9*pi units²
see the attached figure to better understand the problem
the area of the figure ABC is equal to the area of the circle divided by 6
Area figure ABC=9*pi/6-----> (3/2)*pi units²
<span>the area of the shaded portion is equal to
</span>[area of equilateral triangle-3*area figure ABC]
9√3 units²-3*(3/2)*pi units²-----> 9√3 units²-(9/2)*pi units²
the answer is
9√3 units²-(9/2)*pi units²
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