Illustration of odd shape with squares drawn to demonstrate area.

Area of Odd Shapes

Illustration of odd shape with squares drawn to demonstrate area.

Illustration of circles used to find area between two circles (ring).

Area of Circles and Rings

Illustration of circles used to find area between two circles (ring).

Drawing of composite figure with dimensions labeled.

Composite Figure

Drawing of composite figure with dimensions labeled.

Drawing of composite figure with dimensions labeled.

Composite Figure

Drawing of composite figure with dimensions labeled.

Drawing of composite figure with dimensions labeled.

Composite Figure

Drawing of composite figure with dimensions labeled.

Floor plan of room with dimensions labeled.

Floor Plan For Finding Area

Floor plan of room with dimensions labeled.

Floor plan of barn with dimensions labeled. Drawing can be used for area problems.

Floor Plan of Barn for Finding Area

Floor plan of barn with dimensions labeled. Drawing can be used for area problems.

Cross section of steel beam that can be used to find area of composite figures.

Cross Section of Beam

Cross section of steel beam that can be used to find area of composite figures.

Illustration of circle with 10 inch diameter and square.

Circle With 10 inch Diameter and Steel Square

Illustration of circle with 10 inch diameter and square.

Illustration of circle with 6 inch diameter.

Circle With 6 inch Diameter

Illustration of circle with 6 inch diameter.

Illustration of circle with 8 inch diameter.

Circle With 8 inch Diameter

Illustration of circle with 8 inch diameter.

Illustration of circle with parts drawn to show area.

Area of a Circle by parts

Illustration of circle with parts drawn to show area.

Illustration of a circle with squares drawn to demonstrate area.

Area of Circle

Illustration of a circle with squares drawn to demonstrate area.

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle AOB, and the central angle AOB has the same measure as the arc AnB.

Circle With a Chord of 2 ft. and a Radius of 3 ft.

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle…

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Illustration of circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of circle with sector and segment used to find area.

Illustration of partial circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of partial circle with sector and segment used to find area.

Illustration of circle with diameter and segment used to find area.

Circle With Diameter and Segment labeled

Illustration of circle with diameter and segment used to find area.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

Illustration of three circles enclosed in an equilateral triangle.

Circles Enclosed in Equilateral Triangle

Illustration of three circles enclosed in an equilateral triangle.

Illustration of large circle and square with 4 smaller circles inside.

Circles Inside of a Square

Illustration of large circle and square with 4 smaller circles inside.

Illustration of box filled with pipes.

Circular Pipes in Box

Illustration of box filled with pipes.

Illustration of a figure made up of 4 smaller figures (triangles).

Composite Figure

Illustration of a figure made up of 4 smaller figures (triangles).

"A cord of wood is a solidly built pile of 8 feet long, 4 feet wide and 4 feet high. 1. How many cords, stove-wood measure, each stick 12 inches long, could be made from a full-sized cord of wood? 2. If the full cord as pictured above is bought for $3.00 and sawed into stove lengths as in problem (1) and sold for $1.25 a cord, what is the profit? 3. If 6 hours' time was required to saw this wood, and labor cost 25 cents per hour, was there anything gained on the transaction?" -Foster, 1921

Cord of Wood

"A cord of wood is a solidly built pile of 8 feet long, 4 feet wide and 4 feet high. 1. How many cords,…

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches. Being added are 3 equal portions 20x20x5, equaling 2000 cubic inches. The sum of these are 6000. You can find the second portion of the problem <a href="../62392/62392_cube_add2.htm">here</a>.

Cube with Additions 1

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches.…

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be added: three 20x5x5 bars equaling 500 cubic inches and a 5x5x5 (125 cubic inches) cube for the corner. You can find the final cube <a href="../62393/62393_cube_add3.htm">here</a>.

Cube with Additions 2

In order to fill in the spaces from the three 2000 cubic inch additions, four new additions must be…

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625 cubic inches making it a 25x25x25 inch cube equaling 15,625 cubic inches. You can find the original cube <a href="../62391/62391_cube_add1.htm">here</a>.

Cube with Additions 3

This is the final form of the original 20x20x20 inch or 8000 cubic inch cube with the addition of 7625…

Illustration of a ellipse with squares drawn to demonstrate area.

Area of Ellipse

Illustration of a ellipse with squares drawn to demonstrate area.

Illustration of half of an ellipse used to show that the area of an ellipse is equal to pi times a times b.

Area of an Ellipse

Illustration of half of an ellipse used to show that the area of an ellipse is equal to pi times a times…

All triangles formed by a tangent and the asymptotes of an hyperbola are equal in area.

Hyperbola Tangent Triangles

All triangles formed by a tangent and the asymptotes of an hyperbola are equal in area.

Illustration of an irregular figure. To find area, divide round curved portions in small steps with dividers ; add in any straight pieces. "Divide into narrow strips; measure their mid-ordinates. Then - Area = aver. mid-ordinate X length.

Area Of Irregular Figures

Illustration of an irregular figure. To find area, divide round curved portions in small steps with…

This specification discloses a land leveler comprising a massive rectangular frame including reinforced side bars and three crossbars that engage the ground surface for leveling purposes.

Land Leveler

This specification discloses a land leveler comprising a massive rectangular frame including reinforced…

Illustration showing that the area of a parabolic segment made by a chord is two thirds the area of the triangle formed by the chord and the tangents drawn through the ends of the chord.

Tangents and Chords of a Parabola

Illustration showing that the area of a parabolic segment made by a chord is two thirds the area of…

Illustration of parallelogram AEFC drawn two different ways with base b and altitude/height a used to prove the area is aXb.

Area of a Parallelogram

Illustration of parallelogram AEFC drawn two different ways with base b and altitude/height a used to…

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram With Dimensions

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram With Dimensions

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

Parallelogram and Rectangle Relationship

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

"...let the area of the piston a be 1 square inch; of b, 40 square inches. According to Pascal's law, 1 pound placed on a will balance 40 pounds placed on b." &mdash;Hallock 1905

Pascal's Law and Water Pressure

"...let the area of the piston a be 1 square inch; of b, 40 square inches. According to Pascal's law,…

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles and finding the sum of the areas.

Pentagon With Triangular Sections For Area

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles…

Blueprint of Pier/floor plan of Pier with dimensions labeled. Illustration can be used for finding are of composite figures.

Blueprint of Pier

Blueprint of Pier/floor plan of Pier with dimensions labeled. Illustration can be used for finding are…

An illustration of a cross section of a concrete pier for a railway bridge with dimensions labeled. Illustration could be used to calculate volume and area of figures.

Cross Section of Concrete Pier for Railway bridge

An illustration of a cross section of a concrete pier for a railway bridge with dimensions labeled.…

Cross section of pipe, 2 concentric circles

Cross Section of Pipe

Cross section of pipe, 2 concentric circles

Rectangle divided into squares to demonstrate area.

Area of a Rectangle

Rectangle divided into squares to demonstrate area.

Rectangle with squares to show area.

Rectangle With Area Squares

Rectangle with squares to show area.

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

Rectangle With Dimensions

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

An illustration of a rectangle with lengths a and b and area ab.

Rectangle with Lengths a and b with Area ab

An illustration of a rectangle with lengths a and b and area ab.

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration represents the product of c(a+b).

Rectangle with Lengths a, b, and c with Areas ac and bc

An illustration of composite rectangle with lengths a, b, and c with area ac + bc. This illustration…

An illustration of a ring (circle within circle), with diameters of 3a-7 and 6a+9. Illustration could be used to calculate area.

Ring Made of Circles With Diameters 3a-7 and 6a+9

An illustration of a ring (circle within circle), with diameters of 3a-7 and 6a+9. Illustration could…

Illustration of ring (small circle in larger concentric circle).

Ring Made of Concentric Circles

Illustration of ring (small circle in larger concentric circle).

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Ring With Piece Cut Out

Illustration of ring (small circle in larger concentric circle) with piece cut out.

Illustration of ring (small circle in larger concentric circle) sprung into place.

Ring Sprung Into Place

Illustration of ring (small circle in larger concentric circle) sprung into place.

Cross section of road that can be used to find area of composite figures.

Cross Section of Road

Cross section of road that can be used to find area of composite figures.

Scissors roof truss with dimensions labeled.

Roof Truss With Dimensions

Scissors roof truss with dimensions labeled.

Roof truss/floor plan of roof with dimensions labeled.

Roof Truss With Dimensions

Roof truss/floor plan of roof with dimensions labeled.

Gambrel roof truss/floor plan of roof with dimensions labeled.

Gambrel Roof Truss With Dimensions

Gambrel roof truss/floor plan of roof with dimensions labeled.

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center. This illustration can be used to find the area of the zone and the volume of the segments.

Sphere With 8-inch Diameter Cut by Planes

An 8-inch sphere cut by parallel planes, one 2 inches from center and the other 6 inches from center.…

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees, is equal to its spherical excess expressed in angular degrees."

Area of Spherical Triangle

Diagram used to prove the theorem: "The area of a spherical triangle, expressed in spherical degrees,…

Illustration comparing the fundamental units of measure 1 square yard and 1 square meter.

Comparison Of Units Of Square Measure

Illustration comparing the fundamental units of measure 1 square yard and 1 square meter.

An illustration of a hollow square (square within square) with outer square having a side of 2s+6 and inner square having a side of s-2. Illustration could be used for calculating area.

Hollow Square with Dimensions of 2s+6 and s-2

An illustration of a hollow square (square within square) with outer square having a side of 2s+6 and…

Illustration of a trapezoid with altitude a and bases b and b' used to demonstrate that the area is 1/2 the sum of the bases multiplied by the altitude.

Area of a Trapezoid

Illustration of a trapezoid with altitude a and bases b and b' used to demonstrate that the area is…