Journal Chapter 9 10

Journal Chapter 9 10 Jos Pablo Reyes10 5

Describe how to find the areas of a square, rectangle, triangle, parallelogram.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)Examples

Describe how to find the areas of a trapezoid, kite and rhombus.Trapezoid: add the lenght of two parallel sides, then divide by 2 and multiply this by the height

Kite: A=1/2xy

Rhombus: (diagonal 2)(diagonal 1) Describe how to find the area of a composite figure. Explain what a composite figure is.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

Examples

Describe how to find the area of a circle.Area of a Circle: A=(r)

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Describe what a solid is.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 Examples

Describe how to find the surface area of a prism. What is a prism? Explain what a Net is.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

Examples

Describe how to find the surface area of a cylinder.To find the surface area of a cylinder do de following; surface area of a cylinder = 2(r2) + 2(r)(h).

Examples12Describe how to find the surface area of a pyramid. What is a pyramid?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 b, once you know the base area and all faces are the same, do this: Base area + 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

Describe how to find the surface area of a coneTo 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.

Describe how to find the volume of a cubeTo find the surface area of a cube do the following; find the surface area of one side and multiply it by 6.

SA= 6(a)

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Describe Cavalieris principle.If two 3D figures have the same base are and same height, then they will have the same volume

ExamplesDescribe how to find the volume of a prism and a cylinder.Prism: area of base X height Rectangular prism: L x W x H

Cylinder: (r) add the area of the 2 faces, find the area of the bases using the formula A=(r2), the combined surface area of the faces is 2(r2). Then find the surface area of the side which is circumference X height or 2(r)(h).

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Describe how to find the volume of a pyramid and a cone.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 (r)h

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Describe how to find the surface area and volume of a sphereTo find the surface area of a sphere you have to use this formula; 4(r)

To find the volume of a sphere use this formula; 4/3 (r)

Examples