areas of parallelograms and trapezoids. a parallelogram has two sets of parallel lines
TRANSCRIPT
Areas of Areas of Parallelograms and Parallelograms and
TrapezoidsTrapezoids
Areas of Areas of Parallelograms and Parallelograms and
TrapezoidsTrapezoids
• A parallelogram has two sets of parallel lines.
17 feet
12
fee
t
13 fe
et
• The formula for area is A=bh where b is the base and h is the height.
• A=(17)(12)=204 ft2.
17 feet
12
fe
et
• To see the formula visually, cut the end triangle off a parallelogram
• Move the triangle to the other side• The resulting rectangle has the same
area as the parallelogram. • To find the area of a rectangle multiply
the base times the height.
17 feet
12
fee
t
13 fe
et
f igure 3.4
Trapezoids• Trapezoids have one set of parallel
lines and one set of lines that are not parallel.
• The parallel lines are the bases. • The height is perpendicular between
the bases. • The slant heights may be the same or
they may be different.
Trapezoids
• To see how the formula for area works, visualize two of the same trapezoids put together as shown.
• Notice a parallelogram with twice the area of the desired trapezoid.
• The area of the trapezoid is ½ the area of the parallelogram with height the same as that of the trapezoid, and a base that is the sum of the two bases of the trapezoid.
base 1 or b1
base 2 or b2
height
Circumference & Area Circumference & Area of a Circleof a Circle
Circumference & Area Circumference & Area of a Circleof a Circle
The circumference of a circle is
The distance around a circle
Hint: Circumference remember circle around
First we must define some things about a
circle.
The radius is the distance from the center of a circle to any point on a circle.
Hint: I like to define it as halfway through!
The diameter is the distance across a circle through the center.
We use Pi as the measurement to help us find the circumference of a circle.
Pi, not Pie!
HINT: Pi =3.14
Two formulas are used in finding the circumference of a circle.
Circumference = d 3.14 x 4in.
12.6in.
WHEN THE CIRCLE HAS A DIAMETER MEASUREMENT, USE THE FOLLOWING FORMULA.
4in.
Circumference = 2 r
When the radius of a circle is given, the following formula should be used.
2 x 3.14 x 5cm
31.4cm
HINT: Always round your answers to the nearest tenth.
NOW…Let’s have some fun.
Tell me what formula would be used to solve the next five
problems.
3in
C = 2 x 3.14 x r
8ft
C = 3.14 d
122mm
C = 2 x 3.14 x d
17.5 cm
C = 3.14 x d
122.5mm
C = 2 x 3.14 x r
Now that we have determined the correct formula for each, let’s work the problems.
3in
C = 2 x 3.14 x r
The answer is: 18.8in
8ft
C = 3.14 d
The answer is: 25.1ft
122mm
C = 2 x 3.14 x dThe answer is:
766.2mm
17.5 cm
C = 3.14 x d
The answer is: 55cm
122.5mm
C = 2 x 3.14 x r
The answer is: 76,930mm
Classwork & Homework• CW – pg.550 #1-16 evens &
pg.#1-15 odds• WB – pg. 84 & 85