Rodrigo MaselliJournal 9 and 10

Shape Area

Square Length Squared.

Rectangle Length times width.

Triangle Base times height divided by two.

Parallelogram Base times height.

Trapezoid Half of, base one plus base two, times the height.

Kite Half of, diagonal one times diagonal two.

Rhombus Half of, diagonal one times diagonal two.

areas of a square, rectangle, triangle, parallelogram,

trapezoid, kite and rhombus:

Shape Formula

Square L2

Rectangle LW

Triangle BH 2

Parallelogram BH

Trapezoid ½ (b1+b2)H

Kite ½ (d1*d2)

Rhombus ½ (d1*d2)

Formulas for area

Examples

A composite figure is a shape made up of more than one figure.

To find the area of such figure, you need to break it down into pieces and find the area of the broken down shapes.

After this, you need to add the areas you have found.

Composite figures

Examples

The formula for the area of a circle is πr2. Or π(d/2) 2

Pi is an irrational number most of the time stated as 3.14

Area of a circle

Examples

A solid is any three dimensional figure (Height width and depth)

It has sides, edges, faces and corners. Its perimeter is called surface area and its

area is called volume.

Solids

Examples

A prism is a three dimensional shape with two of its bases being congruent figures.

This congruent shapes are connected by parallel lines

The surface area of a prism is the twice the base area of one of the congruent bases plus the lateral area (Length times width of the sides)

A net is a diagram of all of the faces of a prism on the same plane.

Prisms

Examples

A cylinder is made up of two circles connected by a round surface.

To find its surface area you find the area of both of the circles and then of the lateral surface.

The formula to find the surface area of a cylinder is 2 πr 2 + 2πrh

Cylinder

Examples

A pyramid is formed by a shape as a base and triangular faces that meet at a common end point at the top.

To find its surface area, you have to first find the area of the base, then find the area of the sides which are all triangles and add them all up.

The formula to find the surface area of such is: L+B

Pyramids

Examples

A cone is a three dimensional figure formed by a circular base with its lateral face being curved and ending at a common vertex.

To find its surface area you have to find the area of the circle base and then add the lateral surface area

The lateral surface area is found by multiplying the slant height squared by pi.

CONES

Examples

To find the volume of a cube you multiply length times width time the height of the cube.

The formula is L3

Cube

Examples

Cavalieri’s principle states that if on two three dimensional shapes the surface area of the base is the same and the cross sectional area is the same (this including the same height) then the two shapes have the same volume.

Cavalieri’s principle

Assuming they both have the same surface area and exactly the same cross sectional area they have the same volume (drawing not to scale)

EXAMPLES

The volume of a prism is simple, it’s the area of the base times its height.

The formula is V= BH

Volume of a prism

Exampels

The volume of a cylinder is also quite simple, you find the area of the base times its height also.

The area of the base is the area of the circle at the bottom.

VOLUME OF A CYLINDER

Examples

The volume of a pyramid is the same as both past ones just that this one is divided by three.

It is the area of the base, times the height and all of it divided by three (or multiplied by one third)

Volume of a pyramid

Examples

The volume of a cone is the same of that of a pyramid only that the cone has a circular base.

So the volume is found by multiplying the area of the base, times the height divided by three (Or multiplied by one third)

Volume of a Cone

Examples

The surface area of a sphere is found by multiplying four by pi squared.

The formula is 4πr2

Sphere

Examples

The volume of the sphere is simple, you have to multiply four thirds by three, and then by pi cubed.

The formula is 4/3πr3

Volume of a sphere

Examples