Question

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?

Answer 1

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

Explanation:

Answer 2

`73 in.^2`

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:

`A_1=(\pi r^2)/(2)`

where

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

Therefore,

`A_1=(\pi (4)^2)/(2)=25.1 in.^2`

The area of the triangle is given by

`A_2=(1)/(2)bh`

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

`b=16 - 4 = 12 in.`

So the area of the triangle is

`A_2=(1)/(2)(12)(8)=48 in.^2`

So the total area of the figure is

`A=A_1+A_2=25 in^2 + 48 in^2 = 73 in.^2`