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How to calculate the perimeter of a semicircle using 2 simple steps (semicircles)

Updated on March 1, 2013

Perimeter of a semicircle video

To find the perimeter of a semicircle follow these 2 simple steps:

Step 1 First find the arc length of the semicircle (the curved edge of the circle). Do this by multiplying Pi by the diameter of the semicircle and halving your answer. You can summarise this using the following formula.

Arc length of semicircle = ½ × π × d

Step 2 Add the diameter of the semicircle onto your answer from step 1. This will give you the total perimeter of your semicircle. Always remember to do this, as many pupil will make the mistake of only working out the arc length instead of the distance around the whole shape.

Example 1

Find the area of this semicircle of diameter 14 cm.

Step 1

First calculate the length of the arc:

Arc length of semicircle = ½ × π × d

= ½ × π × 14                        (d is 14 as the diameter is 14 cm)

= 21.99 cm (to 2 decimal places)

Step 2

Don’t forget to add on the diameter onto the arc length.

21.99 + 14 = 35.99 cm (2 decimal places).

So the total distance around the edge of the semicircle is 35.99 cm.

Example 2

Work out the perimeter of this semicircle if the radius is 2.5 cm.

Step 1

Again, the first step will be to find the perimeter of the arc. However, in this example you are given the radius instead of the diameter of the semicircle so you will need to double 2.5 to give you the diameter.

d = 2.5 × 2 = 5 cm

Now you can substitute this into the formula to work out the length of the arc.

Arc length of semicircle = ½ × π × d

= ½ × π × 5                           (d is 5 as the diameter is 5 cm)

= 7.85 cm (to 2 decimal places)

Step 2

Now to find the perimeter of the semicircle the final step will be to add the diameter onto the arc length.

7.85 + 5 = 12.85cm (to 2 decimal places)

Therefore the perimeter of the semicircle is 12.85cm.

Summary

Find the arc length of the semicircle using ½ × π × d. Then add the arc length onto the diameter of the semicircle to give you the perimeter of the seimicircle.

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  • catman3000 profile image
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    Mark 4 years ago from England, UK

    To work out the perimeter of semicircle radius 5cm do [(Pi x 10)/2] + 10.

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    leia 4 years ago

    what?! i need help! radius of five?

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    dolly 4 years ago

    IT REALLY HELPS ME A lot

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    littlepanchod 5 years ago

    hey... cool.. ur a don in maths :)

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    kidraulh 5 years ago

    i thinkk u messed up on the addition the addition part was supposed to be 35.98;)

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    Farrukh 5 years ago

    Thanks bro/sis.. (sorry I don't know who u are) This really helps me in solving Geometrical Questions. :) May Almighty Allah bless you.

    Thanks

    Farrukh

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    ;) 6 years ago

    Thank you so much these are really helping. Your explanations are always great and then followed on with actual answers. Great

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