What is the area of Shaded part?
1 answer:
Answer:
1π
Step-by-step explanation:
suppose the radius of semicircle P is r,
then the radius of semicircle Q = (r+d)/2 ... d≤r
radius of semicircle R = (r-d)/2
area P = 1/2 (r)²π
area Q = 1/2 ((r+d)/2)² π = 1/8 (r² + 2rd + d²)π
area R = 1/2 ((r-d)/2)² π = 1/8 (r² - 2rd + d²)π
shaded area = P-Q-R = 1/2 r²π - 1/4 (r² + d²)π
= ((r² - d²)/4) * π
because there is no constant r value in the question and d value changes with the r change, when the vertical segment length equal the semicircle P radius (r), r=2 and d = 0
therefore the shaded area = ((2² -0²)/4)*π = 1π
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Answer:
or 2.738
Step-by-step explanation:
Let’s just look at the triangle on the top with the on the top and x on the bottom. (Basically the top half to the equilateral triangle)
There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem:
We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b= or
Plugging these values into the equation:
x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}
This approximately equals 2.738