José Pablo Reyes 10 – 5

 Square: multiply the base times its self  Rectangle: multiply the base times the height (bxh)  Triangle: multiply the base times the height time half (bxhx1/2)  Parallelogram: multiply the base times the height (bxh)

 Trapezoid: add the lenght of two parallel sides, then divide by 2 and multiply this by the height  Kite: A=1/2xy  Rhombus: ½(diagonal 2)(diagonal 1)

 Composite figure: any figure/shape that can be divided into more than one basic figure. A figure that is made from two or more geometric figures  Area of a composite figure: A=A1+A2

 Area of a Circle: A= π (r²)  Examples:

 A solid is a three dimensional figure, it can me be made up of flat or curve surfaces.  Face: any flat surface in the figure  Edge: segment that is the intersection of two faces  Vertex: point of intersection of 3 or more faces

 Prism: 3D figure formed by two parallel congruent polygonal faces called bases, which are connected by faces that are parallelograms  Net: a diagram of the surfaces of a 3D figure that can be folded to form the figure.  A=2LW + 2(L+W)H

 To find the surface area of a cylinder do de following; surface area of a cylinder = 2 π (r2) + 2 π (r)(h).  Examples

 Pyramid: 3D figure formed by a polygonal base and triangular faces that meet at a common vertex  To find the surface area of a pyramid do the following; find the base area with b², once you know the base area and all faces are the same, do this: Base area + ½ x Perimeter x Slant lenght, if the faces are not the same do this, Base Area + lateral area  Lateral area = all sides that are not the base  Slant lenght = lenght of the segment, from the midpoint of the base to a vertex

 To find the surface area of a cone; find the area of the circle, then turn the shape into its net. Add the measures up and thats the area of the cone.

 To find the surface area of a cube do the following; find the surface area of one side and multiply it by 6.  SA= 6(a²)

 If two 3D figures have the same base are and same height, then they will have the same volume  Examples

 Prism: area of base X height  Rectangular prism: L x W x H  Cylinder: π (r²) add the area of the 2 faces, find the area of the bases using the formula A= π (r2), the combined surface area of the faces is 2 π (r2). Then find the surface area of the side which is circumference X height or 2 π (r)(h).

 To find the volume of a pyramid use the following formula; 1/3 b(h)  To find the volume of a cone use the following formula; 1/3 x π (r²)h

 To find the surface area of a sphere you have to use this formula; 4 π (r²)  To find the volume of a sphere use this formula; 4/3 π (r³)