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1.9 Perimeter, Circumference, and Area

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.

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1.9 Perimeter, Circumference, and Area

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  1. 1.9 Perimeter, Circumference, and Area

  2. s P = 2l+2w or 2(l+w) or l+w+l+w Perimeter = 4s or s+s+s+s Area = s2 l s w A = lw P = s1 + s2 + s3 C = 2r = d r s A = ½ bh h A = r2 b What You'll Learn You will learn to find the perimeter and area for different shapes and the circumference of circles.

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

  4. 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.

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

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

  7. 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

  8. Now lets’ try a circumference: Find the circumference of a circle with a diameter of 12 cm. c = πd • c = π12 • c = 3.14•12 • c = 37.68 cm 12 cm

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

  10. 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

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

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

  13. H = ? 16 in What if you are missing aside ? If the base is 16, and the area is 40, what is the height? A = ½ bh 40 = ½ (16)h 40 = 8h 40/8 = h 5 in = h

  14. Here comes the area of a trapezoid b2= 10 ft • A = ½ (b1+b2)h • A = ½ (6 + 10)(5) • A = ½(16)(5) • A = 40 ft² 5 ft b1= 6 ft

  15. And yet, here’s another area of a trapezoid • A = ½ (8 + 12)(3) • A = ½ (20)(3) • A = 30 km² 12 km 3 km 8 km

  16. 8 km 4 km B2 = ? km Let’s find a missing side If the area of the trapezoid is 24, and the height is 4 and base 1 is 8, what is the other base? A = ½ (h)(b1 + b2) 24 = ½ (4)(8 + x) 24 = 2(8 + x) 24 = 16 + 2x 24 – 16 = 2x 8 = 2x 4 km = x

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

  18. 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

  19. Assignment

  20. Geometry 1.9 Perimeter, Circumference, and Area Find the perimeter and area of each rectangle. Label each measurement. Find the missing measure in each formula if P = 2l + 2w and A = lw. 3 in 6 in 4. l = 4.5, w = 1.5, P = ? 1. 5. l = 2.2, w = 1.1, A = ? 6. l = 12, A = 30, w = ? 7. A = 3½, w = ½, l = ? 1 yd 8. P = 13, w = 2.5, l = ? 2. Find the circumference and area of each circle. Label each measurement. 9. 10. 12 yd 15 cm 3. 1.65 cm 3 m 1.65 cm

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