Semicircle Perimeter Formula
The perimeter of a semicircle includes the curved length (half the circumference of a circle) plus the straight diameter line across its base.
The formula is derived as follows:
- Circumference of a full circle = $2 \pi r$
- Arc length of a semicircle = $\frac{1}{2} \times (2 \pi r) = \pi r$
- Diameter of the semicircle = $2r$
- Perimeter of semicircle = Arc Length + Diameter
- Perimeter = $\pi r + 2r$
- Perimeter = $r(\pi + 2)$
Semicircle Perimeter Calculation
Given values:
- Radius ($r$) = 7 cm
- Value of $\pi$ = $\frac{22}{7}$
Substitute the values into the formula:
Perimeter = $7 \left(\frac{22}{7} + 2\right)$
First, find a common denominator for the terms inside the parentheses:
Perimeter = $7 \left(\frac{22}{7} + \frac{14}{7}\right)$
Add the fractions:
Perimeter = $7 \left(\frac{22 + 14}{7}\right)$
Perimeter = $7 \left(\frac{36}{7}\right)$
Now, multiply:
Perimeter = $\frac{7 \times 36}{7}$
Cancel out the 7s:
Perimeter = $36$ cm
Final Perimeter Value
The calculated perimeter for the semicircle is 36 cm.
Similar Questions
- The ratio of the length to the breath of a rectangular field is $6 : 5$. If the breath is 25 m less than the length, the perimeter of the field is:
- The ratio of the area of an equilateral triangle of side $x$ to the area of a square of side $x$ is:
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- A sector of a circle has a radius of $18\text{ cm}$ and a central angle of $125^\circ$. What will be its approximate perimeter?
(Use $\pi = \frac{22}{7}$) - Area of a square is equal to ten times the area of a rectangle of edge 5 cm $\times$ 8 cm. What is the perimeter of the square?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
- A wire in the form of a circle of radius 56 m is cut and again bent in the form of a square. What is the measure of the diagonal of the square?
- 30 ml paint is required to paint a circular plate of 20 cm radius. How much paint is required to paint a similar plate of radius 80 cm?
- The ratio of the radii of two circles is $1 : 4$. The ratio of their areas is:
- Which of the four options provided below will be the closest to the area of an equilateral triangle, each of whose sides is 10 m long?
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
