Answer:
The answer is 77sq units. approx 28%
210 is the degree of the segment D but its not the area of one angle the opposite side E.
To find the area of a segment we need a formula.
Another way to do this to help you remember is count the radius measure =R2 but what = R2 answer is the points DE
Also we notice FD = R2
and EF also = R
so we have R2+R2 +R =R5
But as they are inwards we now have to draw a triangle point to subtract and then take away the arc circle area which we call arc1 and see a new arc we know it is 2x call that arc2 (means 2 x the value.
The new triangle = 180 degree and measures R1 and R1 add together = 2
We can use 7 + 7 = R1 add R1 as guide example and do the trigonometry
7 x 7 = 49 add the same = 98 square root of 98 = 9.898 which shows a ratio to the 7.
We can express this much better and its important you just write
Example R1 = 5 or R1 = 7 to show an easier ratio.
9.9 rounded to 7 = 1.29 scale enlargement one direction but we need to divide and multiply for all new representation. So we divide 9.898/7 =1.414 this our new scale.
So for showing all sides for the inverse we can write R1, R1, R1 +1.29
Point D:F now is R1+1.29 is hypotenuse which we do need as we split the 180 into 90 2 points to the new arc and find base is now 4.45 if saying R1=7
Like above.or saying base of new arc line = hypotenuse1/2= base 1/2 = R1+0.77 which will be our multiplier. For 3.5, for every line from now on.
Area formula
= 1/2 b x h
= 4.949 x 7 (our radius side)=34.643sq 2
we times this by 2 for the second triangle = 69.286sq2 we
Calculating the Circle
To show area of whole circle and prove for area Pie x R1 x R2 = 3.14 x R1 x R1 so for 7 x 7 = 49sq3 x pi =
Calculating the lower part we want to deduct
= 153.86/2 as one half is below + 2 arcs =1/3 triangle.
=76.93 + 1/3 of 34.623
= 11.51
=88.44
Calculating the Upper part we take away the arc and + x 2 arc we create by drawing another triangle. They are now x3 arc size.
88.44 - 34.623 and - 69.623 = -15.806
We therefore x 1/10 of square R to find the degree
15.806 x 4.9 = 77.494. E angle
Which is the same as 15.806 we just used smaller numbers to represent R and need even smaller numbers now we multiplied.
7 units the radius = 30.003
Compare to the Area of a circle 153.86 and radius R1 = 7
Reverse Area of segment = 77.44 degree.
When we use formula we find A = (½) × r 2 × [(π/180) θ – sin θ]
We check 1/2 x 49 x pi = 24.5 x 3.14 = 76.93 then x 0.0174 then take away the angle you found 90+90-36 = 144 for example when you multiply it to the 0.01174 you find the area.
Explanation: