there are four triangles in a circle . triangles are equal length.5 cm. what is each circles area
Answers
Answer:let us take the radius of the circle to be ‘r'. OF=OE=OD=r
area of triangle BOC= 1/2*BC*OE
=1/2*4*r
=2r cm sq.
Area of triangle AOB= 3/2r cm sq.
Area of triangle AOC=5/2r cm sq.
Now, area of triangle ABC = area of AOB + area of BOC +area of AOC
=3/2r+2r+5/2r
=6r cm sq. ——— let this be equation 1
And, by Heron's formula,
Semi perimeter = (3+4+5)/2
=6 cm
Area of triangle ABC= √s(s-a) (s-b) (s-c)
(s stands for semi perimeter and a, b, c are lengths of sides of the triangle ABC)
= √6(6–3)(6–4)(6–5)
= √6(3)(2)(1)
=√36
=6 cm sq. ——equation 2
Now, equation 1 and 2 are equal because both give the area of triangle ABC
Therefore, 6r cm sq. = 6 cm sq.
6r=6
r=1 cm
So area of circle is π*(1)(1)
=π cm sq.
Hope this helped u understand it clearly. It took a lot of time to write this! But I had so much fun!
Step-by-step explanation: