Semicircle Definition

A semicircle is a half circle. That means a semicircle will certainly have fifty percent of the area the a circle. You might think that means it will certainly have half the perimeter of a circle, however that is not true.

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To make a semicircle, take any type of diameter of the circle. Remove one fifty percent of the circle follow me that diameter. You have actually a semicircle (half of a circle).

A semicircle is fifty percent the circumference of a complete circle add to the diameter of a cricle, (d):

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Learn about the radius, diameter, and circumference that a circle in this lesson.

Table that Contents

Area that a SemicirclePerimeter the a Semicircle

Area the a Semicircle

The area of a semicircle is the space contained through the circle. The area is the variety of square systems enclosed through the political parties of the shape.

The area the a semicircle is always expressed in square units, based on the units used for the radius that a circle.

Area of a Semicircle Formula

The formula because that the area, A, that a one is built approximately its radius. You uncover the area of a semicircle by plugging the given radius the the semicircle into the area of a semicircle formula.

The area formula is:


To discover the area that a semicircle through diameter, divide the diameter by 2 to discover the radius, and then apply the area the a semicircle formula.

How To find The Area of a Semicircle

For example, the semicircle below has a radius that 19 cm. What is the area the the semicircle?

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To uncover its area, we replace r v the yes, really value:

A = πr22

A = π(192)2

A = π(361)2

A = 1134.1149472

A = 567.057 cm2

Area that a Semicircle Example

The roman aqueduct that Barcelona in Spain is very old, date from the first century the the common Era. The aqueduct is an extremely nearly gone, however it has actually semicircular arches still clearly shows on a wall surface in Barcelona.

The arcs measure 2.96 meters in diameter. What is the perimeter and also area of each arch?

P = πr + 2r

P = π(1.48 m) + 2.96 m

P = 4.649557 m + 2.96 m

P = 7.609557 m

Now, we uncover the area:

A = πr22

A = π(1.48m2)2

A = 6.881344 m22

A = 3.440672 m2

Perimeter that a Semicircle

The perimeter of a semicircle is fifty percent the initial circle"s circumference, C, plus the diameter, d. Due to the fact that the semicircle includes a directly side, that is diameter, us cannot define the distance around the form as the circumference of a semicircle; it is a perimeter.

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How To uncover the Perimeter of a Semicircle

Recall that the formula for the perimeter (circumference), C, that a circle of radius, r, is:

C = 2πr

OR

C = πd

To uncover the perimeter, P, that a semicircle, you need fifty percent of the circle"s circumference, plus the semicircle"s diameter:

P = 12(2πr) + d

The 12 and 2 release each other out, for this reason you can simplify to acquire this perimeter that a semicircle formula.

Perimeter the Semicircle Formula

P = πr + d

Using the substitution building of equality, girlfriend can also replace diameter v radius throughout:

P = 12(2πr) + 2rP = πr + 2r

Find The Perimeter of a Semicircle Examples

Let"s shot an example. A semicircle that has a diameter that 100 meters. What is the perimeter?

P = 12(πd) + d

P = 12(π × 100) + 100

P = 12(314.159265) + 100

P = 157.079632 + 100

P = 257.08 meters

It is good to ring the decimal locations as us did here.

Let"s try an instance using the radius of a semicircle. A semicircle has a radius the 365 inches. What is its perimeter?

P = πr + 2r

P = π(365) + 2(365)

P = 1,146.681318 + 730

P = 1,876.68 inches

If the concern asks girlfriend to transform your answer come units prefer feet or yards, convert it; otherwise leave it in the original linear units. Round your answer to every little thing decimal value the difficulty requires.

The semicircles in ~ both ends of an NBA basketball court indicate the limited areas beneath each basket. The semicircles have four-foot radii. What is the perimeter that one semicircle in one restricted area?

P = πr + 2r

P = π(4") + 2(4")

P = 12.56637" + 8"

P = 20.56637"

In this case, having a measurement to 100,000ths that a foot is unnecessary; 20.57" is a reasonably precise answer.

Angle enrolled in a Semicircle

The edge inscribed in a semicircle is always 90°. The inscribed angle is created by illustration a heat from each end of the diameter to any suggest on the semicircle. That doesn"t matter which suggest on the length of the arc, the angle developed where your 2 lines accomplish the arc will constantly be 90°.

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The 2 endpoints that the semicircle"s diameter and also the inscriptions angle will certainly always form a appropriate triangle within the semicircle.