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Using Various puzzle pieces, Marco forms the figure below. What is the best estimate of the area of the figure? F. 146 in? G.77 in? H. 57 in? J. 123 in?

Using Various puzzle pieces Marco forms the figure below What is the best estimate of the area of the figure F 146 in G 77

Answer :

Answer:




The figure shown here consists of two pieces:


- A hemicircle


- A triangle


So, the total area of the figure is the sum of the areas of the two parts.


The area of the hemicircle is given by:




where


r = 4 in. is the radius (half the diameter, which is 8 inches)


Therefore,




The area of the triangle is given by




where


b is the base


h is the height


Here we have:


h = 8 in. is the height


The base is the total length (16 in.) minus the radius of the circle, so




So the area of the triangle is




So the total area of the figure is


Step-by-step explanation:

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Rewritten by : Barada

Answer:

[tex]73 in.^2[/tex]

Step-by-step explanation:

The figure shown here consists of two pieces:

- A hemicircle

- A triangle

So, the total area of the figure is the sum of the areas of the two parts.

The area of the hemicircle is given by:

[tex]A_1=\frac{\pi r^2}{2}[/tex]

where

r = 4 in. is the radius (half the diameter, which is 8 inches)

Therefore,

[tex]A_1=\frac{\pi (4)^2}{2}=25.1 in.^2[/tex]

The area of the triangle is given by

[tex]A_2=\frac{1}{2}bh[/tex]

where

b is the base

h is the height

Here we have:

h = 8 in. is the height

The base is the total length (16 in.) minus the radius of the circle, so

[tex]b=16 - 4 = 12 in.[/tex]

So the area of the triangle is

[tex]A_2=\frac{1}{2}(12)(8)=48 in.^2[/tex]

So the total area of the figure is

[tex]A=A_1+A_2=25 in^2 + 48 in^2 = 73 in.^2[/tex]