Answer:
(a) 21 m squared
(b) 12π cm squared
Step-by-step explanation:
(a) Notice that in order to find the shaded area, we simply need to subtract the little square area from the big triangle's area.
The area of a triangle is: A = (1/2) * b * h, and here, b = 5 and h = 10. So, plugging these in, we have:
A = (1/2 ) * b * h
A = (1/2) * 5 * 10 = (1/2) * 50 = 25 m squared.
The area of a square is simply s * s, where s is the side length. Here, the side length is 2, so s = 2. Plugging this in, we get:
A = s * s
A = 2 * 2 = 4 m squared.
We subtract 4 from 25: 25 - 4 = 21 m squared.
(b) To find the area of the shaded region, we must find the total, big circle area and subtract both small circles' areas from it.
The area of a circle is denoted by: A = [tex]\pi r^2[/tex], where r is the radius.
The second-smallest circle has a radius of 3, so r = 3. Plug this in:
A = [tex]\pi r^2[/tex]
A = [tex]\pi *3^2=9\pi[/tex] cm squared
The smallest circle has a radius of 2, so r = 2. Plug this in:
A = [tex]\pi r^2[/tex]
A = [tex]\pi *2^2=4\pi[/tex] cm squared
Notice that the sum of the diameters of the two small circles add up to the diameter of the big circle. The diameters of the two small circles are 3 * 2 = 6 and 2 * 2 = 4, so adding them together, we see that the big circle's diameter is 6 + 4 = 10. Since radius is half of diameter, the radius of the big circle is 10/2 = 5, so r = 5. Plug this in:
A = [tex]\pi r^2[/tex]
A = [tex]\pi *5^2=25\pi[/tex] cm squared.
Now subtract each of the small circles' areas from this:
[tex]25\pi -9\pi -4\pi =12\pi[/tex]
Thus, the shaded area is 12π cm squared.
Hope this helps!
