The image below is a triangle drawn inside a circle with center O:
8 inches
5 inches
4 inches
Which of the following expressions shows the area, in square inches, of the circle?
(1 = 3.14)
3.14 • 42
3.14 • 52
3.14 • 5
3.14 • 22

3.14 .22 is the product

As product of π x (4.69^2 inches) = 3.14 x 22 = area of 69.08inch^3

This shows the radius of 4.69 squared actually means √22 is the radius. but as it is squared already it becomes the product within the multiplication to find the area.

Area = 3.14  * 22 = 3.14 x 22 = 3.14 . 22

= 69.08inch^3

Step-by-step explanation:

We find the height of a triangle= a^2 + b^2 = c^2.

To check if it is a right angled triangle first step.

c^2= 4^2 x 5^2

c^2 = √16 x √25

c^2 = √400 = 20

Which means this is not a right angle triangle.

If we ignore the 5 inch and draw a line from base 8 = 4 up to vertices of 4inch line we find the lower average of height

c^2 = 16 x 16

c^2 = 256 = 16

We know have the height 16 and 20

We use the difference and can see that 4 is the height.

A=hbb/2

This is the correct way of finding the height, we work on the measures we have and input the half measure into the next measure to find the height along the diameter, then input into a division.

1/2 x 2.5 x 4 =5

1/2 x 8 = height (average)= 4

4/4 x  Hx4/4 =  4

H = 4

So this is the true value of height.

We now know the triangle height is also the radius

As the base fits along the diameter.

We then can calculate the area of the circle given radius 4

Area= pi times the radius squared. So if the radius is 4, then the area is pi times 4squared, which is 16pi. = 50.27inch^2 if it consumed the whole circle then it would be half this 25.135inch

Answers =

3.14 . 42 = 131.88  

3.14 . 52 = 163.28

3.14 . 5 =15.07

3.14 . 22=69.08

If we added the triangle to this area being under 25inch the area combined would be around 4/5 of 25 = 20 so then answer combined would be 4th answer 3.14 . 22

But the question is not combined  so as . means product of x as multiplication must mean 3.14.5 = 3.14 x 5

This would be a completely different radius to what was proved.

4.69 = √22 but as we are multiplying the direct product the answer is 3.14 .22

is the answer.