The area of the shaded region is
.
Solution:
Given radius = 4 cm
Diameter = 2 × 4 = 8 cm
Let us first find the area of the semi-circle.
Area of the semi-circle = 


Area of the semi-circle =
cm²
Angle in a semi-circle is always 90º.
∠C = 90°
So, ABC is a right angled triangle.
Using Pythagoras theorem, we can find base of the triangle.




cm
Base of the triangle ABC =
cm
Height of the triangle = 4 cm
Area of the triangle ABC = 

Area of the triangle ABC =
cm²
Area of the shaded region
= Area of the semi-circle – Area of the triangle ABC
= 
= 
Hence the area of the shaded region is
.
9.6x_12................
10
Answer: 3n+1
(no need to type in the "a_n" or "an" part, as it's already done)
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Explanation:
The first term is a1 = 4 since it is given to us
The common difference is d = 3. This is the value that we add to each term to get the next as the recursive steps shows when we write a(n) = a(n-1)+3
In other words,
nth term = [ (n-1)st term ] + 3
next term = (previous term) + 3
Using a1 = 4 and d = 3, we get the following
an = a1+d(n-1)
an = 4 + 3(n-1)
an = 4+3n-3
an = 3n + (4-3)
an = 3n+1
The box measures 6 by 5 by 4
Area of the top and bottom = 2* (6*5) = 60 square inches
Area of the sides = 2 * (5 * 4) = 40 square inches
Area of front and back = 2 * (6 * 4) = 48 square inches
60 + 40 + 48 = 148 square inches