FORMULAS REVIEW SHEET ANSWERS. 1) SURFACE AREA FOR A PARAMETRIC FUNCTION.
Formulas… They help us find the area. They did not fall out of the sky! In Exploration 10.7, you...
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Transcript of Formulas… They help us find the area. They did not fall out of the sky! In Exploration 10.7, you...
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 1
Base 2
Height
Area of Trapezoids• Method 2: make a 180˚ rotated image;
find the area, and cut it in half.
Base 1
Base 2
Height
Base 1
Base 2
Height
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.
But we use it like this.• Find the perimeter and area of this
triangle.
5 feet
x feet
13 feet
Other ways to make our life easy.
• Compare the circumference and area.
r
2r
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 = 132
x = 12.5•10•12 + 20•10 + .5•π•52
13 “13 “
10 “
10 “
20 “
Try to find the shaded area• Assume the
trapezoidisisosceles.
24 cm
24 cm
38 cm--whole base7 cm
4 cm
• Area of trapezoid - area of parallelogram• Trap: .5 • 24 (24 + 38)• Para: 7 • 4• Did not need
PythagoreanTheorem!
24 cm
24 cm
38 cm--whole base7 cm
4 cm
Find the perimeter and area…
• If it looks right or congruent, it is.
• (1) (2)
9 in.9 in.
18 in.
18 in.
10 m
14 m4 m2
2.8 m
2 m
One• Perimeter
– Sides of largetriangle: 92 + 92 = x2
x = 12.712.7 + 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
9 in.9 in.
18 in.
18 in.
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
10 m
14 m4 m2
2.8 m
2 m