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Area of Semicircle Formula, Definition, Calculate Semi-Circle Area, Examples

Area of Semicircle

A semi-circle is half of a circle. Therefore the Area of Semicircle will be 1/2 πr2. to find the area of a semi-circle, you just have to find the area of a full circle and then divide it by two. It will be helpful to you.

Students often come across a word “semi circle”. So here on this web page of recruitmentresult.com you will get the formula for area of semicircle along with its Definition and examples to Calculate Semi-Circle Area.

Area Of A Semicircle

The area of a semicircle is half the area of the circle from which it is made. Recall that the area of a circle is πr2, where r is the radius.

So, the area of semicircle formula is: Area= 1/2 πr2

Where ‘r’ is the radius of the semicircle and π is Pi, approximately 3.142

Angle Inscribed In A Semicircle

The angle inscribed in a semicircle is always 90°.

Alternative Definition

An alternative definition of a semicircle is that it is simply an arc – a curved line that is half the circumference of a circle, without the straight line linking its ends. This means it is not a closed figure, and so:

  • Has no area
  • Has no perimeter. Its length is the length of the arc, or πr.

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Perimeter of a Semicircle

The perimeter of a semicircle is not half the perimeter of a circle. The perimeter of Semi Circle is the curved part, which is half the circle, plus the diameter line across the bottom.

Recall that the perimeter of a circle is 2πr, so the curved part is half that, or πr, and the base line is twice the radius or 2r.

So, the formula for the perimeter of a semicircle is:

Perimeter= πr+2r OR r (π+2)

Where: r is the radius of the semicircle and π is Pi, approximately 3.142

How to Find: Area of Quadrilateral

Formula of Area of Semicircle

1: Find Radius Of The Semi-Circle: You’ll need the radius to find the area of the semi-circle. Let’s say the radius of the semi-circle is 5 centimeter (2.0 in).

If you’re only given the diameter of the circle, you can divide it by two to get the radius. For example, if the diameter of the circle is 10 centimeter (3.9 in), then you can divide it by 2 (10/2) to get 5 centimeter (2.0 in) as the radius.

2: Find Area Of The Full Circle And Divide It By Two: The formula for finding the area of a full circle is πr2, where “r” represents the radius of the circle. Since you’re finding the area of a semi-circle, you’ll be looking for half of the area of a circle, which means you have to use the formula for finding the area of a semi-circle and then divide it by two.

So, the formula you’ll have to use to find the area of a semi-circle is πr2/2. Now, just plug “5 centimeter (2.0 in)” into the formula to get your answer. You can either use the closest approximation for π with your calculator, substitute 3.14 for π, or you can just leave the symbol in place. Here’s how you do it:

Area = (πr2)/2
Area = (π x 5 cm x 5 cm)/2
Area = (π x 25 cm2)/2
Area = (3.14 x 25 cm2)/2
Area = 39.25 cm2

Check Also: Area of Polygon Formula

3: Remember to state your answer in Square Units: Since you’re finding the area of a shape, you’ll have to use square units (such as cm2) in your answer to indicate that you’re working with a two-dimensional object. If you’re calculating volume, then you’ll be working with cubic units (such as cm3).

Area and Perimeter of Semicircle

Example1: A window in the shape of a semi-circle has a radius of 40 cm. Work out:

  • The area
  • The length of the sealant strip needed for the perimeter

Solution:

Area = 1/2 x π x r2
Area 1/2 x π x 402
Area = 2513 cm2
Perimeter = π x r + 2 x r
Perimeter = π x 40 + 2 x 40
Perimeter = 125.7 + 80
Perimeter = 205.7 cm

Want to Know? How to Find Area of Square

Example2: Find the area of a semicircle with the radius is 5 cm.

Solution:

Given radius = 5 cm.

Formula: Area of the semi circle = 1/2 x π x r2

Here, π = 3.14

= 1/2 π 52cm2
= 1/2 *3.14 * 25 cm2
= 39.25 cm2

The area of the semi circle is 39.25 cm2.

Example 3: Find the area of a semicircle with the radius is 8 cm.

Solution:

Given: radius = 8 cm.

Formula: Area of the semicircle = 1/2 x π x r2

= 1/2 π 82cm2
= 1/2 * 3.14 * 64 cm2
= 100.48 cm2

The area of the semicircle is 100.48 cm2.

Example4: Find the area of the semicircle with the diameter is 14 cm.

Solution:

Given diameter of the semicircle is d = 14 cm.

Formula:

Area of the semi circle = 1/8 * π * d2.

= 1/8 * 3.14 * 142 cm2
= 615.44/8cm2
= 76.93 cm2

The area of the semi circle is 76.93 cm2.

How To Find Area Of Right Angled Triangle: Formula with Examples

Example5: How can I find the area of a semicircle if the whole perimeter is 36cm?

Solution:

Acc to the question: πr + d = 36cm
Where ‘r’ is the radius and’d’ is the diameter
Now, as d = 2r
πr + 2r = 36
(π+2)r = 36
r = 36/(π+2)
r = 36/(22/7 + 2)
r = 7 cm

Now area of circle, as we know is πr²/2

Therefore

Area= π × 7²/2
Area= 77 cm²

Example6: The area of the largest triangle that can be inscribed in a semi-circle of radius x in square unit is:

Solution:

We know that: Area of triangle=1/2×base×height

For the area of the triangle to be both base and height should be of maximum length. The largest length of base that can be chosen is the diameter of the semi-circle. Corresponding to this diameter as base of triangle the longest height that can be chosen is the length of radius as shown in the figure (h1> h2> h3).

Given, Radius of the semi-circle = x units

⇒ Diameter = 2 × radius
= 2x units

∴ Base of triangle, b = 2x units

Also, height of triangle, h = radius of semi-circle

= x units

Hence, area of triangle

=12×b×h=12×b×h
=12×2x×x=12×2x×x
= x2 square units.

Hence, the area of largest triangle that can be inscribed in a semi-circle of radius x units is x2.

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

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