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the figure shown is a rectangle with a semicircle on each end. what is the area of the figure? use 3.14 for [tex]\pi[/tex] and round your answer to the nearest tenth. a. 76.3 [tex]x^{2}[/tex], b. 104.5 in^2, c. 34.8 in^2, or d. 161.0 in^2? PLEASE HELP!

the figure shown is a rectangle with a semicircle on each end what is the area of the figure use 314 for texpitex and round your answer to the nearest tenth a 7 class=

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kudzordzifrancis

Answer:

[tex]\boxed{a.\:\:\:76.3\:in^2}[/tex]

Step-by-step explanation:

The figure is made up of a rectangle and two semicircles.


We find the area of the rectangle using the formula;

[tex]Area = l\times w[/tex]


[tex]\Rightarrow Area = 8\times 6[/tex]


[tex]\Rightarrow Area = 48\:in^2.[/tex]


We find the area of one of the semicircles and multiply by 2;


The area of the semicircles

[tex]=2\times \frac{1}{2}\times \pi \times r^2[/tex]


We substitute [tex]\pi =3.14[/tex] and [tex]r=3\:in[/tex] to obtain;


[tex]=2\times \frac{1}{2}\times 3.14 \times 3^2[/tex]


[tex]= 3.14 \times 9[/tex]


[tex]=28.26\:in^2[/tex]


The area of the figure is

[tex]=48+28.26[/tex]


[tex]=76.26\:in^2[/tex]

To the nearest tenth we have;

[tex]=76.3\:in^2[/tex]

The correct answer is A





wegnerkolmp2741o

Answer:

A = 76.3 in^2

Step-by-step explanation:

We have a rectangle with a semicircle on each end.

We can find the area by adding the areas of each figure

The area of the rectangle is

A = l*w

The length is 8 and the width is 6

A = 8*6 = 48

If we have 2 semicircles ( 2 1/2 circles, we have 1 circle since the diameters are the same)

The area of a circle is

A = pi r^2

The diameter is 6  so the radius is 1/2 of the diameter

r = 1/2 (6) =3

A = pi * (3)^2

A = (3.14) * 9

A = 28.26

The area of the total figure is the area of the rectangle plus the area of the two semicircles ( or 1 circle since the diameters of the semicircle is the same)

A = 48+28.26

A =76.26

To the nearest tenth

A = 76.3 in^2

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