December 2021 Perimeter LO To calculate the perimeter

December 2021 Perimeter LO: To calculate the perimeter of 2 D shapes, circles, and sectors. www. mathssupport. org

Perimeter The perimeter of a closed figure is the total distance around its boundary Polygon The perimeter of a polygon is the sum of the lengths of its sides. For example The perimeter of this polygon is a d b c www. mathssupport. org Perimeter = a + b + c + d

Perimeter Find the perimeter of this figure C 8. 3 m A 12. 4 m B Since it is an isosceles triangle AC = BC = 8. 3 m Perimeter = 8. 3 + 12. 4 Perimeter = 29 m www. mathssupport. org

Perimeter Find the perimeter of this figure C D 4. 2 cm A 8. 4 cm Since it is a rectangle AB = CD = 8. 4 m BC = AD = 4. 2 m Perimeter = 2 8. 4 + 2 4. 2 Perimeter = 16. 8 + 8. 4 Perimeter = 25. 2 cm www. mathssupport. org B

Circumference Circle In the case of the circle, the perimeter is given the special name circumference. We may calculate the circumference of the circle knowing the diameter or the radius. Circumference = pd d Diameter www. mathssupport. org Circumference = 2 pr r radius p Is an irrational number. It is approximately 3. 14159 …

Circumference Find the perimeter of the following figure. r = 7 cm Circumference = 2 pr Circumference = 2 p 7 Exact answer Approximate answer rounded to 3 sf www. mathssupport. org Circumference = 14 p Circumference = 44. 0 cm

Circumference Find the perimeter of the following figure. The figure is made of two semicircles that together make a circle, and two straight sides. The diameter of the circle is the same as the side of the square. 40 m Perimeter = Circumference + 2 Length of each straight side Perimeter = Exact answer Approximate answer rounded to 3 sf www. mathssupport. org pd = ( 40 p ≈ 206 m + 2 40 + 80 )m

Finding the length of an arc What is the length of arc AB? A An arc is a section of the circumference. 6 cm The length of arc AB is a fraction of the length of the circumference. B www. mathssupport. org To work out what fraction of the circumference it is we look at the angle at the centre. In this example, we have a 90° angle at the centre.

Finding the length of an arc What is the length of arc AB? A 6 cm This is because, B 90° 1 = 360° 4 So, = Length of arc AB = 9. 42 cm (to 3 sf) www. mathssupport. org

Finding the length of an arc A B r θ For any circle with radius r and angle at the centre θ, This is the θ Arc length AB = × 2πr circumference 360 of the circle. 2θπr Arc length AB = = 360 180 www. mathssupport. org

Finding the length of an arc Find the perimeter of the following sector. For the perimeter of the sector we need the length of the arc. 120° 8 cm We add the length of the arc with the two radii. Perimeter = Length of arc + 2 radius θ × 2πr + 2 r Perimeter = 360 120 × 2π 8 + 2 8 Perimeter = 360 Perimeter = www. mathssupport. org ≈ 32. 8 cm

The perimeter of shapes made from arcs Find the perimeter of these shape on a cm square grid: The perimeter of this shape is made from three semicircles. Perimeter = 3π + 2π + π Perimeter = 6π cm ≈ 18. 9 cm (to 3 sf. ) www. mathssupport. org

The perimeter of shapes made from arcs Find the perimeter of these shape on a cm square grid: 40° Perimeter = 3+3 Perimeter = 6 Perimeter = 2π + 6 ≈ 12. 3 cm (to 3 sf. ) www. mathssupport. org

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