Pre Algebra ( period 1)

Chapter 10 Area & Volume
AREA-
all these formulas are related to the basic concept of A = bh
Area of Parallelograms 10-1

Area of rectangles and parallelograms = (base)(height)


Triangles & Trapezoids 10-2
Area of triangle = (1/2)(base)(height or altitude)


Area of trapezoid = (average of the 2 bases)(height)


Now we're starting area!
Where the perimeter/circumference fenced in my puppy, the area of the yard will tell me how much sod (grass) I should buy to stop the puppy's paws from getting muddy!

Area for me is all basically the length of the base times the height of the figure

A = bh

In a parallelogram, whether it's a rectangle, rhombus, square or other parallelogram

A = bh with the height being a line perpendicular to both bases (not the slanted side!)


You have learned the area of a rectangle as A = lw, but the l = b and the w = h

You may have learned the area of a square as A = s² , but that's because the b = h


Any parallelogram can be split into 2 triangles using a diagonal.

Because of this, the area of a triangle is half that of a parallelogram.

A = 1/2 bh


A trapezoid has 2 bases that ARE NOT EQUAL. So which base is THE base?

If you use the smaller base, you won't have enough sod for your yard and the puppy's paws are still getting muddy.

If you use the larger base, you'll have too much sod for your yard and the extra will rot.

Sooooooooo..... you actually need to take the average of the two bases times the height

A = (average of the 2 bases)(height)

A = (b₁ + b₂)h /2

Space Figures 10-4
SPACE FIGURES OR SOLIDS OR 3 DIMENSIONAL FIGURES
 (solids)
prisms = 2 congruent parallel bases - all other sides are rectangles

cylinder = 2 congruent circle bases

When you remove one base from a prism, it becomes a pyramid - all other sides are triangles

When you remove one base from a cylinder, it becomes a cone

When you have a set of points in all directions that are equal distance from a central point, you have a sphere

Vertices - the points where edges connect (the corners)

Edges - the line segments that connect the vertices


You should be able to visualize what a figure will look like if you could cut it apart and open it

That's called a net!
We'll look at some of these in class together.

Try to think of what it will form if you fold it back up!