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

If the height of a trapezoid is 3m, and b1 is 4 m, and b2 is 8 m, what is the area?

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

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Area of a trapezoid
Area of a Parallelogram

10.2-Areas of Circles

formula to get the area and circumference of a circle

area of a circle- A=3.14*r squared

10.2 Vocab

Area- The amount of space inside of the boundary of a flat object

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

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Find the area of the circle

The answer is ....

More Examples

Diameter=6

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

Solid-three-dimensional figure that encloses a part of space

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

What is this??...

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

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Answer -

10.4(Surface Areas of Prisms and Cylinders)

Formula

lateral surface area-2*3.14*r*h

Surface area of a cylinder- 2*2.14*r*r+2*3.14*r*h

Vocab

net-two-dimensional pattern that forms a solid when it is folded

surface area- the sum of the areas of its faces

Examples

At the Myraid Botanical Gardens in Oklahoma City, a tropical conservatory bridges a small lake. The Crystal Bridge is a cylinder 224 feet long and 70 feet in Diameter. Find the surface area of the Crystal Bridge, including bases. Round to the nearest tenth.


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

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This is what?

It is a rectangular pyramid

10.5(Surface areas of pyramids and cones)

Formula

Surface area of a pyramid using a net- surface area=area of base+(number of triangles*area of each triangle)

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

slant height-the height of a lateral face,that is, any face that is not the base

Examples

Your school needs a square pyramid with a base with a base for a play. Each side of the base will have a length of 10 feet. The slant height will be 15 feet. How many square feet of material are needed to build this pyramid?


Answer-400 feet

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10.6(Volume of Prisms and Cylinders)

Formula

Volume of a prism- V=Bh

Volume of a cylinder-V=3.14*r*r*h

Vocab

volume- the amount of space it occupies

Examples

Find the volume of the cylinder using the radius and the height

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

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10.7-(Volumes of Pyramids and Cones

Vocab

pyramid- this is a polyhedron. Pyramids have one base. The other faces are triangles

cone- a solid with on circular base

volume- a measure of the amount of space the solid occupies

Examples

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10.8(volume of a sphere)

Vocab

volume-A measurement of how much space the solid occupies

sphere-a solid formed by all points in space that are fixed same distance from a fixed point called the center

Examples

The radius of the sphere is 4 m. What is the volume?





The sphere below shows a sphere with the radius of 14. What would be the volume of this sphere?

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