Geometry Formulas

• Geometry formulas work just like the ones we did when we were doing algebra.

• Remember, a formula is a rule:• Jill always takes twice as long to get ready as

she says she will. (Actual time) = 2 x (what Jill said).

• No matter what the actual time was or how long she said she’d take, the relationship between the two numbers stays the same.

Area Formulas

• The main ones to know are square, rectangle and triangle. We’ll go over circle formulas a little later, and if you need parallelogram or trapezoid, just use the formula provided on the formulas page as shown above.

Area Formulas

• Area is the ENTIRE INSIDE of a shape• It is always measured in “squares” (sq. inch, sq

ft)

Area Formulas

• Find the area of a rectangle with a length of 8 inches and a width of 12 inches:

• Step 1) Write the formula you need• Area = length x width or A = LW• Step 2) Substitute numbers for variables

wherever possible:• A = 8 x 12

Area Formulas

• Find the area of a rectangle with a length of 8 inches and a width of 12 inches:

• A = 8 x 12• Step 3) Solve• A = 96• The area of the rectangle is 96 inches.

Area Formulas

• Find the area of the rectangle:11’

4’

Area Formulas

• Find the area of the rectangle:11’

4’

Step 1) A = LWStep 2) A = 4x11Step 3) A = 44The area of the rectangle is 44 feet.

Area Formulas• Find the length of the rectangle:

x

6cmArea = 42 cm

Area Formulas• Find the length of the rectangle:

x

6cm Area = 42 cm

Step 1) A = LWStep 2) 42 = L(6)Step 3) ÷6 ÷6

7 = L

Area Formulas

• Area of a square • Formula:

• Area = s2

• Note that a square is a type of rectangle. • s2 means multiply the side times the side, right?

That’s the same as length times width, but, with a square, the length and the width are always the same, so we can use this shortcut.

Area of Squares/Rectangles

• Area = Length x Width or Area = s2

2

Length(2) xWidth(2) = 4 square units

Area Formulas

• Find the area of the square:

5 in.

Area Formulas

• Find the area of the square:

5 in.

A = s2

A = 52

A = 25

Area Formulas

• Find the length of a side of this square:

Area = 36

Area Formulas

• Find the length of a side of this square:

Area = 36

A = s236 = s2√36 = s The measurement6 = s of the side is 6.

Area Formulas

• All geometry formulas work with the exact same 3 steps:

1) write the formula you need2) substitute numbers for variables3) solve• There’s no new math here!

Area Formulas

• Area of a triangle:• Area = ½ x base x height• A = ½ BH or A = .5BH

height

base

Area Formulas

• Find the area of the triangle:

4cm

3 cm

Area Formulas

• Find the area of the triangle:

4cm

3 cmA = ½ BHA = ½ x 3 x 4

Area Formulas• Find the area of the triangle:

4cm

3 cm

A = ½ BH A = ½ BHA = ½ x 3 x 4 A = ½ x 3 x 4A = ½ x 12 A = 2 x 3A = 6 A = 6

Pause

• You may want to pause the presentation here and try the practice problems on pages 154 and 155 in your book.

Perimeter Formulas

• Perimeter is the distance around a shape. Certain shapes, such as squares and rectangles, have formulas to find the perimeter. In some irregular shapes, we must add all of the sides together to find the perimeter. The word rim, meaning edge, is inside the word perimeter which makes it easy to remember what the word means.

• Perimeter of a rectangle:• Perimeter = 2 x length + 2 x width• P = 2L + 2W

• Perimeter of a rectangle:• Perimeter = 2 x length + 2 x width• P = 2L + 2W

+

Perimeter Formulas

• Find the perimeter of the rectangle:

6 feet 2 feet

Perimeter Formulas

• Find the perimeter of the rectangle:

6 feet 2 feet

P = 2L + 2WP = 2(6) + 2(2)P = 12 + 4P = 16

• Find the length of the rectangle:

3”Perimeter = 24”

P = 2L + 2W

• Find the length of the rectangle:

3” Perimeter = 24”

P = 2L + 2W24 = 2L + 2(3)24 = 2L + 6-6 -618 = 2L÷2 ÷29 = L

Perimeter

• Triangles have 3 sides…add up each side’s length.

88

8

8+8+8=24The Perimeter is 24

Pause

• Try the practice perimeter problems on page 156 of your book.

Volume Formulas

Volume formulas

• Volume of a cube

Volume formulas

• Volume of a cube• V = s3

• V = 6x6x6• V = 216

Volume formulas

• Volume of a rectangular solid:• V = length x width x height

Volume formulas

• Volume of a rectangular solid:• V = length x width x height• V =LWH• V = 6x3x2• V = 36

Volume formulas

Find the length of a rectangular solid with a height of 4 meters, a width of 6 meters and a volume of 96 cubic meters.

Volume formulas

Find the length of a rectangular solid with a height of 4 meters, a width of 6 meters and a volume of 96 cubic meters.

V = LWH 96 = L(6)(4) 96 = L x 24÷24 ÷244 = L

Geometry Formulas

• Try the practice problems on page 157 in the book and check your answers online.