Chapter 11 Areas of Plane Figures (page 422)

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Presentation transcript:

Chapter 11 Areas of Plane Figures (page 422) How can you calculate the area of any figure?

Lesson 11-1 Areas of Rectangles (page 423) Essential Question How can you calculate the area of any figure?

Area is measured in square units. Areas of Rectangles vs. Rectangle Rectangular Region Area is measured in square units. u2 vs. u

The area of a square is the square of the length of a side . Postulate 17 The area of a square is the square of the length of a side . A = s2 s

Also, the perimeter of a square is 4 times the length of a side. P = 4s s s s

If two figures are congruent, then they have the same area . Postulate 18 If two figures are congruent, then they have the same area .

Postulate 19 The area of a region is the sum of the areas of its non-overlapping parts.

Any side of a rectangle (parallelogram) can be considered to be a base (b).

Any segment perpendicular to the line containing the base from any point on the opposite side is an altitude . b

The length of an altitude is called the height (h). b

The area of a rectangle equals the product of its base and height. Theorem 11-1 The area of a rectangle equals the product of its base and height. A = bh h b

OR, the area of a rectangle equals the product of its length & width. A = ℓw w ℓ

The perimeter of a rectangle equals the twice length + twice width. ℓ P = 2ℓ + 2w w w ℓ … P = 2b + 2h

Example #1 The area of a square is 9 sq. cm. Find its perimeter.

Example #2 The perimeter of a rectangle is 20 cm Example #2 The perimeter of a rectangle is 20 cm. If its height is 4 cm, find its area. 4 cm b

Example #3 Consecutive sides of the figure are perpendicular Example #3 Consecutive sides of the figure are perpendicular. Find its area. 4 6 9 3 7 5 1

Example #3 Consecutive sides of the figure are perpendicular Example #3 Consecutive sides of the figure are perpendicular. Find its area. 9 3 6 4 7 16 u2 4 5 1 1 9

Example #3 Consecutive sides of the figure are perpendicular Example #3 Consecutive sides of the figure are perpendicular. Find its area. 9 3 6 4 99 u2 11 7 16 u2 4 5 1 1 9

Example #3 Consecutive sides of the figure are perpendicular Example #3 Consecutive sides of the figure are perpendicular. Find its area. 9 3 6 4 99 u2 35 u2 7 16 u2 4 5 1 1 9

Example #3 Consecutive sides of the figure are perpendicular Example #3 Consecutive sides of the figure are perpendicular. Find its area. 9 3 6 4 99 u2 35 u2 7 16 u2 4 5 1 1 9 A = 16u2 + 99u2 + 35u2 = 150u2

How can you calculate the area of any figure? Assignment Written Exercises on pages 426 & 427 RECOMMENDED: 1 to 15 odd numbers REQUIRED: 17 to 31 odd numbers 32, 34 UPDATE YOUR STUDENT AID CARD! How can you calculate the area of any figure?