Mathematics, 28.01.2020 07:31 luceridiaaz

Asemi-circle sits on top of a rectangle to form the figure below. find its area and perimeter. use 3.14 for ππ .. 4 in l, base 6in

Asemi-circle sits on top of a rectangle to form the figure below. find its area and perimeter. use 3

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Answer from: mya1318

The area of the given figure is 38.13 in² and its perimeter is 23.42 in.

First, we will determine the area of the semicircle,

Area of a semicircle = Half area of a circle

Area of a circle = $\pi r^{2}$

∴ Area of semicircle = $\frac{1}{2}\pi r^{2}$

Where r is the radius

From the diagram, the base of the figure (length of the rectangle) equals the diameter of the semicircle

∴ diameter = 6 in.

But

$radius = \frac{diameter}{2}$

∴ $radius = \frac{6}{2}$

r = 3 in.

Now, from

Area of semicircle = $\frac{1}{2}\pi r^{2}$

Area of the semicircle = $\frac{1}{2} \times 3.14 \times 3^{2}$

Area of the semicircle = $1.57 \times 9$

Area of the semicircle = 14.13 in².

For the rectangle,

Area of rectangle = $length \times width$

Length = 6 in.

and the width = 4 in.

∴ Area of the rectangle = 6 × 4

Area of the rectangle = 24 in².

Now, for the area of the figure,

Area of the figure = Area of the semicircle + Area of the rectangle

∴ Area of the figure = 14.13 in². + 24 in².

Area of the figure = 38.13 in².

For the perimeter of the figure,

Perimeter is sum of all sides

∴ Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference

First, we will determine the length of the half circumference,

Length of the half circumference = $\frac{1}{2}\times2\pi r = \pi r$

Length of the half circumference = 3.14 × 3

Length of the half circumference = 9.42 in.

From

Perimeter of the figure = Width of rectangle + Length of rectangle + Width of rectangle + length of the half circumference

∴ Perimeter of the figure = 4 in. + 6 in. + 4 in. + 9.42 in.

Perimeter of the figure = 23.42 in.

Hence, the area of the figure is 38.13 in² and its perimeter is 23.42 in.

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Asemi-circle sits on top of a rectangle to form the figure below. find its area and perimeter. use 3

Answer from: kingsqueen883

Check the picture below.

Answer from: Quest

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation:

Answer from: Quest

$x=2\sqrt{10}$

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

$6^2+2^2=x^2$

simplifying:

$6^2+2^2=x^2\\36+4=x^2\\40=x^2\\x=\sqrt{40}$

to further simplify this radical, we need to use the property $\sqrt{x*y}=\sqrt{x} \sqrt{y}$

thus

$x=\sqrt{40}\\ x=\sqrt{4}\sqrt{10} \\ x=2\sqrt{10}$

What is the value of x? leave your answer in simplest radical form.

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Asemi-circle sits on top of a rectangle to form the figure below. find its area and perimeter. use 3...