Area of Semicircle given diameter of semicircle SolutionSTEP 0: Pre-Calculation Summary STEP 1: Convert Input(s) to Base Unit Diameter: 10 Meter --> 10 Meter No Conversion Required STEP 2: Evaluate Formula STEP 3: Convert Result to Output's Unit 39.2699081698724 Square Meter --> No Conversion Required Credits Softusvista Office (Pune), India Team Softusvista has created this Calculator and 600+ more calculators! Bhilai Institute of Technology (BIT), Raipur Himanshi Sharma has verified this Calculator and 900+ more calculators!
3 Semicircle CalculatorsArea of Semicircle given diameter of semicircle FormulaArea = (pi*(Diameter)^2)/8 What is area of a semicircle when diameter is given?The area of a semicircle when the diameter is given is the region occupied by the semicircle in a two-dimensional plane of diameter "d". A semicircle is a half-circle. That means a semicircle will have half of the area of a circle. Therefore, 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. How to Calculate Area of Semicircle given diameter of semicircle?Area of Semicircle given diameter of semicircle calculator uses Area = (pi*(Diameter)^2)/8 to calculate the Area, Area of Semicircle given diameter of semicircle is the area enclosed by a semicircle of diameter d. Area is denoted by A symbol. How to calculate Area of Semicircle given diameter of semicircle using this online calculator? To use this online calculator for Area of Semicircle given diameter of semicircle, enter Diameter (d) and hit the calculate button. Here is how the Area of Semicircle given diameter of semicircle calculation can be explained with given input values -> 39.26991 = (pi*(10)^2)/8. FAQWhat is Area of Semicircle given diameter of semicircle? Area of Semicircle given diameter of semicircle is the area enclosed by a semicircle of diameter d and is represented as A = (pi*(d)^2)/8 or Area = (pi*(Diameter)^2)/8. Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere. How to calculate Area of Semicircle given diameter of semicircle? Area of Semicircle given diameter of semicircle is the area enclosed by a semicircle of diameter d is calculated using Area = (pi*(Diameter)^2)/8. To calculate Area of Semicircle given diameter of semicircle, you need Diameter (d). With our tool, you need to enter the respective value for Diameter and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well. How many ways are there to calculate Area? In this formula, Area uses Diameter. We can use 2 other way(s) to calculate the same, which is/are as follows -
In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts. So, we can write the formulas of area and perimeter for a semicircle using the area and perimeter of a circle. In this article, you will learn how to identify a semicircle and find the area and perimeter of a semicircle with the help of formulas and solved examples. What is a Semi-Circle?A semicircle is formed when a
lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a circular shape. Semi Circle ShapeWhen a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape. Since a semicircle is half that of a circle, hence the area will be half that of a circle. In the below figure, the line AC is called the diameter of the circle. The diameter divides the circle into two halves such that they are equal in area. These two halves are referred to as the semicircles. A circle is a locus of points equidistant from a given point which is the centre of the circle. The common distance from the centre of a circle to its point is called a radius. Thus, the circle is entirely defined by its
centre (O) and radius (r). The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7. Area of Semicircle = 1/2 (π r2) DerivationAs defined above, the area of a semicircle is half of the area of a circle. Also, we can say that the area of a circle is the number of square units inside that circle. Let us generate the above figure. This polygon can be broken into n isosceles triangle (equal sides being radius). Thus, one such isosceles triangle can be represented as shown below. The area of this triangle is given as ½(h*s) Now for n number of polygons, the area of a polygon is given as ½(n*h*s) The term n × s is equal to the perimeter of the polygon. As the polygon gets to look more and more like a circle, the value approaches the circle circumference, which is 2 × π × r. So, substituting 2×π×r for n × s. Polygon area = h/2(2 × π × r) Also, as the number of sides increases, the triangle gets narrower and so when s approaches zero, h and r have the same length. So substituting r for h: Polygon area = h/2(2 × π × r) = (2 × r × r × π)/2 Rearranging this we get Area = πr2 Now the area of a semicircle is equal to half of that of a full circle. Therefore, Area of a semicircle = (πr2)/2 Perimeter of SemicircleThe perimeter of a semicircle is the sum of half of the circumference of the circle and its diameter. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius. Therefore, The perimeter of Semicircle = (1/2) π d + d Or Circumference = (πr + 2r) Semi circle FormulaThe below table shows the formulas associated with the semicircle of radius r.
Video Lessons on CirclesIntroduction to CirclesParts of a CircleArea of a CircleAll about CirclesSemi circle ExamplesExample 1: Find the area of a semicircle of radius 28 cm. Solution: Given, Radius of semi circle = r = 28 cm Area of semi circle = (πr2)/2 = (½) × (22/7) × 28 × 28 = 1232 Therefore, the area of the semi-circle is 1232 sq. cm. Example 2: What is the perimeter of a semicircle with a diameter of 7 cm? Solution: Given, Diameter of semicircle = d = 7 cm Formula for the circumference (perimeter) of a semicircle using its diameter = (½)πd + d Substitute the value of d, we get; = (½) × (22/7) × 7 + 7 = 11 + 7 = 18 Therefore, the perimeter of the semicircle is 18 cm. Practice Problems
Frequently Asked Questions on SemicircleYes, a semicircle is half the circle. That means a circle can be divided into two semicircles. The shape of a semicircle will be obtained by cutting a circle along its diameter and the full arc of a semicircle always measures 180 degrees. An example of a semicircular shape is a protractor.
The angle made by the triangle in a semicircle is a right angle, i.e. 90 degrees. The area of a semicircle with radius r is equal to half the area of the circle. The perimeter formula of the semicircle of radius r is given by: What is the area of a semicircle with a diameter of 8?8^2 is 64, so A = 3.14 * 64/2. Simplified, that's A = 200.96/2, which is 100.48. Therefore, the area of this semicircle is 100.48 square inches.
What is the area of a semicircle with diameter 12 cm?When reporting the final answer remember the units of area must be squared, giving a final answer of 56.52 cm2.
|
How to find the area of a semicircle with the diameter
Related Posts
Copyright © 2024 muatrau Inc.
