Answer:
See below
Step-by-step explanation:
Outline
- First find the diameter, LN. Then find the radius, NO
- Then find the area of the semi circle LMN
- Finally the area of the triangle.
- Subtract semi circle and triangle.
Step One
The Pythagorean Theorem says a^2 + b^2 = r^2
- <N = 180 - 90 - 45 Property of a triangle
- a = b = 4 The triangle is isosceles Two 45o angles
- 4^2 + 4^2 = c^2 Expand
- 16 + 16 = c^2 Add
- 32 = c^2 Take the square root of both sides
- sqrt(c^2) = sqrt(32)
- c = sqrt(16 * 2)
- c = 4 * sqrt(2)
- The diameter of the circle is 4 sqrt(2)
- The radius =d/2 = 4 * sqrt(2)/2 = 2 sqrt(2)
Step Two
Find the area of the of the Semi Circle
Formula
Solution
- Area = pi * (2*sqrt(2) )^2 / 2
- Area = pi * 4 * 2 / 2
- Area = 4 pi
Step 3
Find the area of the triangle.
Area
The two legs are at right angles and they both = 4
- Area = b*h/2
- Area = 4*4/2
- Area = 8
Step Four
Area shaded part = 4pi - 8
There are all kinds of possible answers. Here are a couple
- Area= 4(pi - 2)
- Area = 4pi - 8
- Area= 4.56
If none of these are among your choices, leave a note.
