Area+&+Volume

**__AREA & VOLUME__**

**//__ Area __//** - The area of a figure is the number of square units it encloses.


 * //__ Altitude __//** - An altitude is any segment perpendicular to the linecontaining the base of a figure, and drawn from the side opposite the base.

**//__Altitude of triangle__//** - The perpendicular sement from a vertex of a triangle to the line containing the opposite side. The height is the length of the altitude.

A = 1/2 bh
 * //__ Area of a Triangle __//** - The area of a triangle equals half the product of any base length b and the corresponding height h.

**//__ Area of a Trapezoid __//** - The area of a trapezoid is half the product of the height and the sum of the length of the bases. A = 1/2 h ( b1 + b2 )

**//__ Area of a circle __//** - The area of a circle equals the product of pi and the square of the radius r. A = pi(r)2

EX. cylinder, a cone,prism, and etc.
 * //__ Space figures(Solids) __//**  - Three-dimensional figure or solid.

**//__ Prism __//** - Has 2 parallel bases that are congruent polygons, and lateral faces that are parallelograms.

__**// Pyramid //**__ - Has a base that is a polygon. The lateral faces are triangles.


 * //__ Cylinder __//** - Has 2 parallel bases that are congruent circles.


 * //__ Cone __//** - Has 1 circular base and one vertex.

__//** Sphere **//__ - The set of all points in spaces that are a given distance from a given point called the center.


 * //__ Net __//** - A pattern you can form into a space figure.

S.A. = L.A. = 2B←(area of a base)
 * //__ Surface Area(S.A.) __//** - The sum of the areas of the base(s) and lateral faces of a space figure.

__//** Lateral Area(L.A.) **//__  - The lateral area of a prism is the sum of the areas of the lateral faces. L.A. = ph ← (p)perimeter x (h)height

__//**Surface area of a cylinder**//__ - The lateral area of a cylinder is the product of the circumference of the base and the height of the cylinder. <span style="background-color: #ff00ff; font-family: 'Comic Sans MS',cursive;"> L.A. = 2(pi)(r)(H). <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive;">The surface area of a cylinder is the sum of the lateral area and the areas of the 2 bases.

__//** Slant height **//__ - You can use the slant height of a face, to finds the area of the lateral faces. If n is the number of lateral triangular faces, <span style="background-color: #ff00ff; font-family: 'Comic Sans MS',cursive;">L.A.is n(1/2bl)

<span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive; font-size: 120%;">__//** Volume **//__ - The volume of a space figure is the number of cubic units needed to fill it. <span style="background-color: #ff00ff; font-family: 'Comic Sans MS',cursive;">V = Bh ← Base area x height

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive;">**//__Cubic Unit__//** <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive;">- The amount of space occupied by a cube with sides one unit long.


 * //__<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive;">Volume of a Cone and of a Pyramid __//** - The formula for volume of a cone or a pyramid is 1/3 the base area B times the height h. <span style="background-color: #ff00ff; font-family: 'Comic Sans MS',cursive;">V = 1/3 Bh

<span style="background-color: #ffff00; font-family: 'Comic Sans MS',cursive;">**//__Volume of a Sphere__//** <span style="background-color: #ffffff; font-family: 'Comic Sans MS',cursive;">- The volume V of a sphere with radius //r// is 4/3pi times the cube of the radius.