Two semicircles are drawn in a 14 by 7 rectangle. Find the area of the blue region.
+505 To answer this question, you will need to find the area of the chord of a circle with a radius of 7, shown in the image below, and then multiply by 2
The area of the chord is the area of the sector minus the area of the triangle:
\(\frac{49\pi}{3}-3.5\sqrt{3}\cdot3.5\cdot\frac{1}{2}\cdot2 \)
=\(\frac{49\pi}{3}-12.25\sqrt{3}\)
Now, multiply that by 2 and the answer is \(\frac{98\pi}{3}-25\sqrt{3}\)
That is roughly equal to 59.324
+128475 See the following :
We have 30-60-90 triangle GIF where GI = 3.5 and IF = 3.5sqrt (3)
So....the area of this triangle is (1/2) (3.5)(3/5) sqrt (3) = (49/4)sqrt (3)/2 (1)
And then we have the area of 60° sector of a circle with a rdius of 7 less a triangle with sides of 7 and an included angle of 60°
So this area is (1/2)7^2 ( pi/3) - (1/2) ( 7)^2 sqrt (3) / 2 = (49/2) ( pi/3 - sqrt (3) / 2) =
49pi/6 - (49/4) sqrt (3) (2)
So 1/4 area of this shaded region is (1) + (2) = (49/6) pi - (49sqrt (3) /8)
So....the total area is 4 [ (49/6) pi - 49sqrt (3) / 8 ' =
(98/3) pi - (49/2) sqrt (3) ≈ 60.19 units^2
Exactly what Guest found !!!
