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Formulas…

Formulas…

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Formulas…

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  1. Formulas… • They help us find the area. • They did not fall out of the sky! • In Exploration 10.7, you will develop the formulas for the area of a triangle, rectangle, and parallelogram. • Now, let’s develop the formula for the area of a trapezoid.

  2. Area of Trapezoids • First method: draw a diagonal, and find the area of 2 triangles. Base 2 Height Base 1

  3. Area of Trapezoids • Method 2: make a 180˚ rotated image; find the area, and cut it in half. Base 2 Base 1 Height Height Base 2 Base 1

  4. Area of a circle • If you like, read Exploration 10.8. It explains in more detail why the area of a circle is πr2.

  5. Take any circle. • Subdivide it into many congruentsectors--in this case,we made 16.

  6. Cut out each sector. Rearrange them. • What shape does this remind you of? • What is the formula for finding the area of this shape? Find it!

  7. Pythagorean Theorem • The most proved theorem ever--over 300 proofs! One was done by James Garfield, before he was president of the United States. • If you have a right triangle with hypotenuse of length “c”, then a2 + b2 = c2.

  8. It looks like this! • a2 + b2 = c2.

  9. 13 feet 5 feet x feet But we use it like this. • Find the perimeter and area of this triangle.

  10. r 2r Other ways to make our life easy. • Compare the circumference and area.

  11. 13 “ 13 “ 10 “ 10 “ 20 “ Try this--find perimeter and area

  12. 13 “ 13 “ 10 “ 10 “ 20 “ • P = tri + rect + sem13 + 13 + 10 + 20 + 10 + sem (.5 • 2π• 5) • A = tri + rect + sem52 + x2 = 132x = 12.5•10•12 + 20•10 + .5•π•52

  13. 38 cm--whole base 7 cm 4 cm 24 cm 24 cm Try to find the shaded area • Assume thetrapezoidisisosceles.

  14. 38 cm--whole base 7 cm 4 cm 24 cm 24 cm • Area of trapezoid - area of parallelogram • Trap: .5 • 24 (24 + 38) • Para: 7 • 4 • Did not needPythagoreanTheorem!

  15. 2 m 4 m2 14 m 2.8 m 18 in. 9 in. 10 m 9 in. 18 in. Find the perimeter and area… • If it looks right or congruent, it is. • (1) (2)

  16. 18 in. 9 in. 9 in. 18 in. One • Perimeter • Sides of largetriangle: 92 + 92 = x2 x = 12.7 12.7 + 12.7 + 12.7 + 12.7 + 9 + 9 = 68.6 in. • Area: Note that the largetriangle can be moved to make a rectangular figure. • 9 • 18 = 162 in.2

  17. 2 m 4 m2 14 m 2.8 m 10 m Two • Perimeter: • 10 + 10 + 2.8 + 2.8+ 2.8 + 2.8 + 2 + 2 =35.2 m • Area: • Two trapezoids and a rectangle • (.5)(2)(10 + 14) + (.5)(2)(10 + 14) + 2 • 14 • 84 m2