Geometry Concepts Explained: Perimeter, Area, and Circles
Starter
Which of these shapes has the greatest perimeter?
Which has the smallest?
What is each perimeter in terms of
d
?
Answers
Square has 4 sides of length
d
4
d
Hexagon has 6 sides of ½
d
3
d
Answers
Square has 4 sides of length
d
4
d
Hexagon has 6 sides of ½
d
3
d
Circle is between 3
d
and 4
d
π
d
Which of these shapes has the greatest area?
Which has the smallest?
What is the area in terms of
r
?
Area
Large square is 2r x 2r = 4r
2
Small square is half of this = 2r
2
Area
Large square is 2r x 2r = 4r
2
Small square is half of this = 2r
2
Circle has area in between 2r
2
and 4r
2
Area
Circles
A circle has radius
r
.
Rearrange the sectors.
Circles
Circumference of circle = 2
π
r
Length of half circumference =
π
r
So the length of this side is
π
r
Consider the lengths.
Circles
Radius of circle =
r
So the height is
r
π
r
Consider the lengths.
Circles
Area of shape is close to area of
parallelogram
= base x height
=
π
r
x
r
=
π
r
2
r
π
r
Hence the area of a circle is =
π
r
2
Consider the area.
Circles
A circle has radius
r
and diameter
d.
Circumference of a circle
C =
π
d
Area of a circle
A =
π
r
2
Circles
Calculate the
area
and
perimeter
of the following shapes:
d = 4cm
r = 6cm
r = 4cm
r = 7cm
r = 6cm
r = 4cm
r = 1.5cm
r = 2cm
1/8
r = 3cm
45°
60°
r = 8cm
r = 3cm
225°
r = 5cm
165°
Answers
A = 6.28cm²
A = 14.14cm²
A = 12.57cm²
A = 38.48cm²
P = 10.28cm
P = 15.42cm
P = 14.28cm
P = 25.00cm
A = 28.27cm²
A = 37.70cm²
A = 3.53cm²
A = 1.57cm²
P = 21.42cm
P = 26.85cm
P = 7.71cm
P = 5.57cm
A = 3.53cm²
A = 33.51cm²
A = 17.67cm²
A = 36.00cm²
P = 8.36cm
P = 24.38cm
P = 17.78cm
P = 24.40cm
Calculate the
area
and
perimeter
of this compound shape:
8cm
12cm
Calculate the
area
and
perimeter
of this compound shape:
8cm
12cm
Area of rectangle = b x h
Area of rectangle = 8 x 12
Area of rectangle = 96cm²
96cm²
Calculate the
area
and
perimeter
of this compound shape:
8cm
12cm
96cm²
Area of semi-circle =
π
x r
²
÷
2
Area of semi-circle =
π
x 6
²÷
2
Area of semi-circle = 56.55cm²
56.55cm²
Calculate the
area
and
perimeter
of this compound shape:
8cm
12cm
96cm²
56.55cm²
Area of semi-circle =
π
x r
²
÷
2
Area of semi-circle =
π
x 4
²÷
2
Area of semi-circle = 25.13cm²
25.13cm²
Calculate the
area
and
perimeter
of this compound shape:
8cm
12cm
96cm²
56.55cm²
Total area =
96 + 56.55 + 25.13 =
177.68cm
²
25.13cm²
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.
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Presentation Transcript
Starter Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d? d d d
Answers Square has 4 sides of length d Hexagon has 6 sides of d 4d 3d d d d d d
Answers Square has 4 sides of length d Hexagon has 6 sides of d Circle is between 3d and 4d 4d 3d d
Area Which of these shapes has the greatest area? Which has the smallest? What is the area in terms of r? r r r
Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2 r r r 2r
Area Large square is 2r x 2r = 4r2 Small square is half of this = 2r2 Circle has area in between 2r2 and 4r2
Circles A circle has radius r.
Circles Rearrange the sectors.
Circles Consider the lengths. So the length of this side is r Circumference of circle = 2 r Length of half circumference = r
Circles Consider the lengths. r So the height is r Radius of circle = r
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
Circles A circle has radius r and diameter d. r Circumference of a circle C = d d Area of a circle A = r2
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
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
Calculate the area and perimeter of this compound shape: 8cm 12cm
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
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
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
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
