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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. Area of Trapezoids.

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## Formulas…

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**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.**Area of Trapezoids**• First method: draw a diagonal, and find the area of 2 triangles. Base 2 Height Base 1**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**Area of a circle**• If you like, read Exploration 10.8. It explains in more detail why the area of a circle is πr2.**Take any circle.**• Subdivide it into many congruentsectors--in this case,we made 16.**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!**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.**It looks like this!**• a2 + b2 = c2.**13 feet**5 feet x feet But we use it like this. • Find the perimeter and area of this triangle.**r**2r Other ways to make our life easy. • Compare the circumference and area.**13 “**13 “ 10 “ 10 “ 20 “ Try this--find perimeter and area**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**38 cm--whole base**7 cm 4 cm 24 cm 24 cm Try to find the shaded area • Assume thetrapezoidisisosceles.**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!**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)**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**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

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