1.9 perimeter, circumference, and area
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1.9 Perimeter, Circumference, and Area. s. P = 2l+2w or 2(l+w) or l+w+l+w. Perimeter = 4s or s+s+s+s Area = s 2. l. s. w. A = lw. P = s 1 + s 2 + s 3. C = 2 r = d. r. s. A = ½ bh. h. A = r 2. b. What You'll Learn. - PowerPoint PPT PresentationTRANSCRIPT
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You will learn to find the perimeter and area
for different shapes and the circumference
of circles.s
s
Perimeter = 4s or
s+s+s+s
Area = s2
l
w
P = 2l+2w or
2(l+w) or
l+w+l+w
A = lwb
h s
P = s1 + s2 + s3
A = ½ bhr
C = 2r = d
A = r2
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What is a perimeter?
• Perimeter is the distance all the way around an object.
• The perimeter of a circle is called the circumference.
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How To Find Perimeter
Find the length of each side of the object.
Add all the lengths of the sides together.
This total is the perimeter.
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Lets’ find the perimeter.
8 + 4 + 8 + 4 = 24.
This rectangle has a perimeter of 24.
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How about this perimeter ?
6 + 5 + 5 + 6 + 12 = 34.
This pentagon has a perimeter of 34.
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Now lets’ try a circumference:
• c=2πr or c=πd
• r = radius (half the distance across a circle)
• d = diameter (the distance across a circle)
• Note that 2r = d
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Find the circumference of a circle with a diameter of 12 cm.
c = πd
• c = π12
• c = 3.14•12
• c = 37.68 cm
12 cm
Now lets’ try a circumference:
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Find the circumference of a circle with a radius of 3
meters.
3 m
Lets’ try aother circumference:
• c = 2πr
• c = 2π3• c = 2 • 3.14 • 3
• c = 18.84 m
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What if we know the circumference ?
If the circumference of a circle is approximately 50.3 cm, find the radius. (Use 3.14 for π)
C = 2•π•r
50.3 = 6.28r 50.3 / 6.28 = r
8 cm r
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Time for area.
• Area of a rectangle• A = bh• A = 4(2)• A = 8 cm²
4 cm
2 cm
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Not done yet!!
• Area of a triangle:• A = ½ bh• A = ½ (6)(7)• A = 21 mm²
7 mm
6 mm
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What if you are missing aside ?
If the base is 16, and the area is 40, what is the height?
16 in
H = ?40 = ½ (16)h
40 = 8h
40/8 = h
5 in = h
A = ½ bh
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Here comes the area of a trapezoid
• A = ½ (b1+b2)h
• A = ½ (6 + 10)(5)• A = ½(16)(5)• A = 40 ft²
b2= 10 ft
b1= 6 ft
5 ft
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And yet, here’s another area of a trapezoid
• A = ½ (8 + 12)(3)• A = ½ (20)(3)• A = 30 km²
8 km
12 km
3 km
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If the area of the trapezoid is 24, and the height is 4 and base 1
is 8, what is the other
base?
B2 = ? km
8 km
4 km
Let’s find a missing side
24 = ½ (4)(8 + x)24 = 2(8 + x)24 = 16 + 2x
24 – 16 = 2x8 = 2x
4 km = x
A = ½ (h)(b1 + b2)
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Just one more, the area of a circle
• A = πr²
• A = 3.14(10)²
• A = 3.14(100)
• A = 314 m²
10 m
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OK, one last area of a circle.
• Diameter = 8 in• Radius = 4 in• A = 3.14(4)²• A = 3.14(16)• A = 50.24 in²
8 in
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Assignment
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1.9 Perimeter, Circumference, and Area
Geometry
Find the perimeter and area of each rectangle. Label each measurement.
1.6 in
3 in
2.
1 yd
12 yd
3.1.65 cm
1.65 cm
4. l = 4.5, w = 1.5, P = ?
Find the missing measure in each formula ifP = 2l + 2w and A = lw.
5. l = 2.2, w = 1.1, A = ?
6. l = 12, A = 30, w = ?
7. A = 3½, w = ½, l = ?
8. P = 13, w = 2.5, l = ?
Find the circumference and area of each circle. Label each measurement.
9.
10.
15 cm
3 m