 # 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 = s 2 l w P =

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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 = s 2 l w P = 2l+2w or 2(l+w) or l+w+l+w A = lw b h s P = s 1 + s 2 + s 3 A = ½ bh r C = 2  r =  d A =  r 2

What is a perimeter? Perimeter is the distance all the way around an object. The perimeter of a circle is called the circumference.

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.

Lets’ find the perimeter. 8 + 4 + 8 + 4 = 24. This rectangle has a perimeter of 24.

How about this perimeter ? 6 + 5 + 5 + 6 + 12 = 34. This pentagon has a perimeter of 34.

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

Find the circumference of a circle with a diameter of 12 cm. c = πd c = π  12 c = 3.1412 c = 37.68 cm 12 cm Now lets’ try a circumference:

Find the circumference of a circle with a radius of 3 meters. 3 m Lets’ try aother circumference: c = 2πr c = 2  π  3 c = 2 3.14 3 c = 18.84 m

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 = 2πr 50.3 = 6.28r 50.3 / 6.28 = r 8 cm  r

Time for area. Area of a rectangle A = bh A = 4(2) A = 8 cm² 4 cm 2 cm

Not done yet!! Area of a triangle: A = ½ bh A = ½ (6)(7) A = 21 mm² 7 mm 6 mm

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

Here comes the area of a trapezoid A = ½ (b 1 +b 2 )h A = ½ (6 + 10)(5) A = ½(16)(5) A = 40 ft² b 2 = 10 ft b 1 = 6 ft 5 ft

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

If the area of the trapezoid is 24, and the height is 4 and base 1 is 8, what is the other base? B 2 = ? 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 = 2x 8 = 2x 4 km = x A = ½ (h)(b 1 + b 2 )

Just one more, the area of a circle A = πr² A = 3.14(10)² A = 3.14(100) A = 314 m² 10 m

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

Assignment

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 4. l = 4.5, w = 1.5, P = ? Find the missing measure in each formula if P = 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

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