Geometry Concepts Explained: Perimeter, Area, and Circles

Explore the concepts of perimeter, area, and circles through comparisons of shapes such as squares, hexagons, and circles. Understand how to calculate perimeters and areas in terms of given variables like side lengths and radii. Dive into the properties of circles including circumference, area, and diameter.

• Geometry
• Perimeter
• Area
• Circles
• Shapes

senan Follow

Uploaded on Aug 03, 2024 | 0 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

Presentation Transcript

1. Starter Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d? d d d

2. Answers Square has 4 sides of length d Hexagon has 6 sides of d 4d 3d d d d d d

3. Answers Square has 4 sides of length d Hexagon has 6 sides of d Circle is between 3d and 4d 4d 3d d

4. Area Which of these shapes has the greatest area? Which has the smallest? What is the area in terms of r? r r r

5. Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2 r r r 2r

6. Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2 Circle has area in between 2r2 and 4r2

7. Circles A circle has radius r.

8. Circles Rearrange the sectors.

9. Circles Consider the lengths. So the length of this side is r Circumference of circle = 2 r Length of half circumference = r

10. Circles Consider the lengths. r So the height is r Radius of circle = r

11. Circles Consider the area. r r Area of shape is close to area of parallelogram Hence the area of a circle is = r2 = base x height = r x r = r2

12. Circles A circle has radius r and diameter d. r Circumference of a circle C = d d Area of a circle A = r2

13. Calculate the area and perimeter of the following shapes: r = 6cm r = 7cm d = 4cm r = 4cm r = 1.5cm 1/8 r = 4cm r = 2cm r = 6cm r = 3cm 60 45 165 r = 5cm 225 r = 8cm r = 3cm

14. Answers A = 6.28cm P = 10.28cm A = 14.14cm P = 15.42cm A = 12.57cm P = 14.28cm A = 38.48cm P = 25.00cm A = 28.27cm P = 21.42cm A = 37.70cm P = 26.85cm A = 3.53cm P = 7.71cm A = 1.57cm P = 5.57cm A = 3.53cm P = 8.36cm A = 33.51cm P = 24.38cm A = 17.67cm P = 17.78cm A = 36.00cm P = 24.40cm

15. Calculate the area and perimeter of this compound shape: 8cm 12cm

16. Calculate the area and perimeter of this compound shape: 8cm Area of rectangle = b x h Area of rectangle = 8 x 12 12cm 96cm Area of rectangle = 96cm

17. Calculate the area and perimeter of this compound shape: 56.55cm 8cm Area of semi-circle = x r 2 Area of semi-circle = x 6 2 12cm 96cm Area of semi-circle = 56.55cm

18. Calculate the area and perimeter of this compound shape: 56.55cm 8cm Area of semi-circle = x r 2 Area of semi-circle = x 4 2 12cm 96cm Area of semi-circle = 25.13cm 25.13cm

19. Calculate the area and perimeter of this compound shape: 56.55cm 8cm Total area = 96 + 56.55 + 25.13 = 12cm 96cm 177.68cm 25.13cm