Answer: The area is 24 square units.
Step-by-step explanation:
Things you need to use in this exercise:
Area of a circle = pi*r^2
r is the radius, equal to half the diameter.
Ok, in the image we can see 3 half-circles.
one has a diameter of 8 units: with area A (the left one)
other has a diameter of 6 units: with area B (the bottom one)
and the other has a diameter equal to the hypotenuse of the right triangle: with area C (the white semicircle that also includes the right triangle)
Now, you can think the shaded area as:
The sum of the areas of the half circles A and B, minus the area of the half-circle C, plus the area of the right triangle (because the white triangle is also included in the white semicircle)
So the area is:
A + B - C + area triangle
A = pi*(8/2)^2 = 3.14*4^2 = 50.24
B = pi*(6/2)^2 = 3.14*3^2 = 28.26
the area of the triangle is equal to:
T = 6*8/2 = 24
Now, to obtain the area of the white semicircle ( C) we need the hypotenuse of the triangle, so here we can use the Pythagorean's theorem:
H^2 = 8^2 +6^2
H = √(8^2 + 6^2) = 10
Then:
C = pi*(10/2)^2 = 3.14*5^2 = 78.5
Then the shaded area is:
Area = 50.24 + 28.26 + 24 - 78.5 = 24
