Area of a Semicircle | Formula, Definition & Perimeter

Semicircle Definition

A semicircle is a half circle. That means a semicircle will have half of the area of a lap. You might think that means it will have half the margin of a circle, but that is not true .
To make a semicircle, take any diameter of the set. Remove one half of the r-2 along that diameter. You have a semicircle ( half of a r-2 ) .
A semicircle is half the circumference of a wax lap plus the diameter of a cricle, ( vitamin d ) :
Semicircle Definition

Learn about the spoke, diameter, and circumference of a circle in this lesson .

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Area of a Semicircle

The area of a semicircle is the space contained by the circle. The area is the number of public square units enclosed by the sides of the form .
The area of a semicircle is constantly expressed in feather units, based on the units used for the radius of a traffic circle .

Area of a Semicircle Formula

The formula for the area, A, of a encircle is built around its spoke. You find the area of a semicircle by plugging the given radius of the semicircle into the area of a semicircle recipe .
The area convention is :

A = πr22

To find the area of a semicircle with diameter, divide the diameter by 2 to find the spoke, and then apply the area of a semicircle rule .

How To Find The Area of a Semicircle

For example, the semicircle downstairs has a radius of 19 curium. What is the area of the semicircle ?
Area of a Semicircle Formula
To find its area, we replace r with the actual value :
A = πr22
A = π ( 192 ) 2
A = π ( 361 ) 2
A = 1134.1149472
A = 567.057 cm2

Area of a Semicircle Example

The Roman aqueduct of Barcelona in Spain is identical old, dating from the first century of the Common Era. The aqueduct is identical closely gone, but it has semicircular arches still visible on a wall in Barcelona .
The arches measure 2.96 meters in diameter. What is the margin and area of each arch ?
P = πr + 2r
P = π ( 1.48 molarity ) + 2.96 megabyte
P = 4.649557 meter + 2.96 megabyte
P = 7.609557 megabyte
now, we find the area :
A = πr22
A = π ( 1.48m2 ) 2
A = 6.881344 m22
A = 3.440672 m2

Perimeter of a Semicircle

The perimeter of a semicircle is half the original circle ‘s circumference, C, plus the diameter, d. Since the semicircle includes a true side, its diameter, we can not describe the distance around the condition as the circumference of a semicircle ; it is a perimeter .
Perimeter of a Semicircle Definition

How To Find the Perimeter of a Semicircle

echo that the formula for the margin ( circumference ), C, of a circle of radius, r, is :
C = 2πr
OR
C = πd
To find the margin, P, of a semicircle, you need half of the encircle ‘s circumference, plus the semicircle ‘s diameter :
P = 12 ( 2πr ) + d
The 12 and 2 cancel each other out, so you can simplify to get this perimeter of a semicircle convention .

Perimeter of Semicircle Formula

P = πr + vitamin d
Using the substitution place of equality, you can besides replace diameter with radius throughout :

  • P = 12 ( 2πr ) + 2r
  • P = πr + 2r

Find The Perimeter of a Semicircle Examples

Let ‘s try an exemplar. A semicircle that has a diameter of 100 meters. What is the circumference ?
P = 12 ( πd ) + five hundred
P = 12 ( π × 100 ) + 100
P = 12 ( 314.159265 ) + 100
P = 157.079632 + 100
P = 257.08 meters
It is fine to round the decimal places as we did here .
Let ‘s try an example using the radius of a semicircle. A semicircle has a radius of 365 inches. What is its circumference ?
P = πr + 2r
P = π ( 365 ) + 2 ( 365 )
P = 1,146.681318 + 730
P = 1,876.68 inches
If the wonder asks you to convert your answer to units like feet or yards, convert it ; otherwise leave it in the original analogue units. Round your answer to whatever decimal value the problem requires .
The semicircles at both ends of an NBA basketball woo indicate the qualify areas beneath each basket. The semicircles have four-foot radius. What is the circumference of one semicircle in one qualify area ?
P = πr + 2r
P = π ( 4 ‘ ) + 2 ( 4 ‘ )
P = 12.56637’ + 8 ‘
P = 20.56637 ‘
In this lawsuit, having a measurement to 100,000ths of a foot is unnecessary ; 20.57 ‘ is a reasonably accurate answer.

Angle Inscribed in a Semicircle

The angle autograph in a semicircle is always 90°. The inscribe angle is formed by drawing a production line from each end of the diameter to any point on the semicircle. It does n’t matter which point on the duration of the discharge, the angle created where your two lines meet the bow will constantly be 90° .
The two endpoints of the semicircle ‘s diameter and the inscribe slant will always form a right triangulum inside the semicircle .

Next Lesson:

Area of a Sector of a circle

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