Chapter 10
Stephanie Windau
10.1-Areas of Parallelograms and Trapezoids
10.1-- Vocab
Base of a Parallelogram-the length of any one of its sides
Height of a parallelogram-the perpendicular distance between the opposite side
Base of a trapesoid-its two parallel sides
Height of a trapezoid- the perpendicular distance between the bases
10.1-- Examples
The formula for a trapezoid is, .5(b1+b2)h, so you would input the numbers so that you can solve the question. The formula is now, .5(4+8)3=A, then you solve, the answer to this question is, A=18m squared.
If the height of a parallelogram is 3 cm, and the base is 5 cm, what is the area?
The formula to a parallelogram is base*height=area. You then input the numbers, 3*5=A, then you solve for the area. The area of this parallelogram is 15 cm.
The trapezoid below is the next problem that we are going to solve.
You have the b1, b2, and the height.
Input the numbers into the formula.
.5(10+18)9=A
A=126
10.2-Areas of Circles
formula to get the area and circumference of a circle
10.2 Vocab
Circle-a round plane figure whose boundary consists of points equidistant from a fixed point
radius- a straight line from the center to the circumference of a circle or sphere
diameter- a straight line passing from side to side through the center of a body or figure, especially a circle or sphere
circumference- the enclosing boundary of a curved geometric figure, especially a circle
pi- 3.14159265358
Find the area of the circle
The answer is ....
More Examples
Radius=3
Use 3.14 for pi
First you would insert the numbers into the equation- 3.14*(3*3)
then solve- the answer is 28.26
10.3- Three-Dimensional Figures
Vocab
polyhedron-a solid that is enclosed by polygons
face-polygons that form a polyhedron
prism-a solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figure, and whose sides are parallelograms
pyramid-this has one base and the other faces are triangles
cylinder-a solid geometric figure with a straight parallel sides and a circular or oval cross section
cone-a solid or hollow object that tapers from a circular or roughly circular base to a point
sphere-a round solid figure with every point on its surface equidistant from its center
edge-the segments where faces of a polyhedron meet
vertex-a point where tree or more edges meet
Examples
I come with something very sweet. Kids love to eat me after a cold snack. I usually come with Ice cream?
Answer-Cone
What am I?...
I bounce very easily. Without me, most sports wouldn't be able to function.
Answer-Sphere
Answer -
10.4(Surface Areas of Prisms and Cylinders)
Formula
Surface area of a cylinder- 2*2.14*r*r+2*3.14*r*h
Vocab
surface area- the sum of the areas of its faces
Examples
Answer-56,957.1
Find the surface area using B(area of the base),P(perimater of base),and the h(height)
B= 4 inch, P=8 in, h=5 in.
Answer=48 in
This is what?
It is a rectangular pyramid
10.5(Surface areas of pyramids and cones)
Formula
Area of a lateral surface of a cone using a net- A=3.14*r*l
Surface area of a Cone-S=3.14*r*r+3.14*r*l
Vocab
Examples
Answer-400 feet
10.6(Volume of Prisms and Cylinders)
Formula
Volume of a cylinder-V=3.14*r*r*h
Vocab
Examples
r=4 ft., h=11 ft.
answer-552.9
find th volume of the rectangular prism with lenth, width, and height
l=6 m., w=2 m., h=11 m.
answer-132 m3
10.7-(Volumes of Pyramids and Cones
Vocab
cone- a solid with on circular base
volume- a measure of the amount of space the solid occupies
Examples
10.8(volume of a sphere)
Vocab
sphere-a solid formed by all points in space that are fixed same distance from a fixed point called the center
Examples
The sphere below shows a sphere with the radius of 14. What would be the volume of this sphere?