Perimeter worksheet

1. Circumference (perimeter): 43.98 mm

1. The perimeter of a circle is its circumference, 2π times the radius

   $\text{C = 2πr}$

2. Put in your radius

   $C$$=2\times \pi \times 7$$=43.982297\text{\hspace{0.17em}mm}$

2. Circumference (perimeter): 37.7 yd

1. The perimeter of a circle is its circumference, 2π times the radius

   $\text{C = 2πr}$

2. Put in your radius

   $C$$=2\times \pi \times 6$$=37.699112\text{\hspace{0.17em}yd}$

3. Perimeter: 20 km

1. All four sides of a square are equal, so the perimeter is four times one side

   $\text{P = 4s}$

2. Put in your side length

   $P$$=4\times 5$$=20\text{\hspace{0.17em}km}$

4. Perimeter: 23 yd

1. The perimeter of any four-sided shape is the sum of its four sides

   $P$$=7+5+5+6$$=23\text{\hspace{0.17em}yd}$

5. Perimeter: 10 yd

1. First check the sides can meet: the longest side must be shorter than the other two added together (the triangle inequality)

   $\text{4 < 6}$

2. The perimeter of a triangle is the sum of its three sides

   $P$$=2+4+4$$=10\text{\hspace{0.17em}yd}$

3. For reference, Heron's formula gives the area from the sides, using half the perimeter, s

   $A$$=\sqrt{5\times \left(5-2\right)\times \left(5-4\right)\times \left(5-4\right)}$$=3.872983$

6. Perimeter: 15 units

1. First check the sides can meet: the longest side must be shorter than the other two added together (the triangle inequality)

   $\text{6 < 9}$

2. The perimeter of a triangle is the sum of its three sides

   $P$$=3+6+6$$=15\text{\hspace{0.17em}units}$

3. For reference, Heron's formula gives the area from the sides, using half the perimeter, s

   $A$$=\sqrt{7.5\times \left(7.5-3\right)\times \left(7.5-6\right)\times \left(7.5-6\right)}$$=8.714213$

7. Perimeter: 15.71 m

1. Each side is the straight-line distance between neighbouring corners. Square the change in x and in y, add them and take the square root. The last corner joins back to the first

   $\text{side = √(Δx² + Δy²)}$

2. Side from corner 1 to corner 2

   $\mathrm{s1}$$=\sqrt{{\left(8-2\right)}^2+{\left(2-2\right)}^2}$$=6$

3. Side from corner 2 to corner 3

   $\mathrm{s2}$$=\sqrt{{\left(2-8\right)}^2+{\left(5-2\right)}^2}$$=6.708204$

4. Side from corner 3 to corner 1

   $\mathrm{s3}$$=\sqrt{{\left(2-2\right)}^2+{\left(2-5\right)}^2}$$=3$

5. Add all the sides

   $P$$=6+6.708204+3$$=15.708204\text{\hspace{0.17em}m}$

6. For reference, the shoelace formula gives the area inside, which is correct when the sides don't cross

   $A$$=9$

8. Perimeter: 30 cm

1. Add the 5 side lengths

   $P$$=5+7+6+4+8$$=30\text{\hspace{0.17em}cm}$

9. Perimeter: 42 in

1. A regular polygon has n equal sides, so its perimeter is n times one side

   $\text{P = n × s}$

2. Put in the number of sides and the side length

   $P$$=6\times 7$$=42\text{\hspace{0.17em}in}$

3. For reference, the area is half the perimeter times the apothem a (centre to the middle of a side), where a = s ÷ (2·tan(180° ÷ n))

   $A$$=\frac{1}{2}\times 42\times 6.062178$$=127.305734$

10. Perimeter: 20 ft

1. All four sides of a square are equal, so the perimeter is four times one side

   $\text{P = 4s}$

2. Put in your side length

   $P$$=4\times 5$$=20\text{\hspace{0.17em}ft}$