 | Thomas Tate (mathematical master.) - 1848 - 284 pages
...c part ADB; thereby showing that the rectangle is double the triangle. From this theorem it follows that the area of a triangle is equal to half the area of a rectangle having the same base and perpendicular height : hence we have the following rule for the... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...having equal altitudes, that has the greater area which has the greater base. THEOREM VI. 299. The area of a triangle is equal to half the area of the parallelogram formed from any two of its sides, having an angle equal to that between those sides.... | |
 | James Bates Thomson - Arithmetic - 1882 - 416 pages
...Scalene Triangle is one having all its sides unequal. AREA OF TRIANGLES. 808. It is proved by Geometry that The area of a triangle is equal to half the area of a parallelogram of equal base and altitude. ILLUSTRATION. —Let ABCD be a parallelogram whose altitude... | |
 | William Dodds - 1883 - 198 pages
...rectangle ADGF. Therefore the whole triangle ABC is equal to half the rectangle EBGF. Hence it follows that the area of a triangle is equal to half the area of a rectangle having the same base and perpendicular height. Ex. In the triangle ABC, the base BC-8 ft.,... | |
 | Euclides - 1883 - 176 pages
...draw to two parallel straight lines two straight lines = and JL one another. 16. The area of a rhombus is equal to half the area of the rectangle contained by its two diagonals. 17. In AB, the hypotenuse of a right-angled triangle ABC, take any point D and draw... | |
 | John Tilden Prince - Arithmetic - 1894 - 148 pages
...the area of a rhomboid. 6. Show by diagram how to find the area of a trapezoid. 7. Show by diagram that the area of a triangle is equal to half the area of a parallelogram of the same base and altitude. 8. A garden in the form of a parallelogram has a length... | |
 | John Tilden Prince - Arithmetic - 1895 - 358 pages
...the area of a rhomboid. 6. Show by diagram how to find the area of a trapezoid. 7. Show by diagram that the area of a triangle is equal to half the area of a parallelogram of the same base and altitude. 8. A garden in the form of a parallelogram has a length... | |
 | George Chrystal - Algebra - 1898 - 476 pages
...AC.BD-AD.BC = 0; or AC.BD = AB.CD + AD.BC, wherein AC, etc., now denote absolute lengths, and AC.BD, etc., absolute areas. § 90. The fundamental theorem...the area of a trapezium is ^(a + b)h, where a and Ь denote its parallel sides, and h denotes the distance between these sides. This formula is often... | |
 | Edward L. Bates, Frederick Charlesworth - Geometry - 1912 - 648 pages
...Triangles on ihe same, or equal, bases, and having the same height, are equal in area. Again, since the area of a triangle is equal to half the area of the parallelogram on the same base and having the same height, the theorem above can be extended to triangles,... | |
 | Richard Courant, Herbert Robbins - Juvenile Nonfiction - 1996 - 596 pages
...numbers pr and qr respectively, and then letting pr and qr tend to p and q. It is geometrically obvious that the area of a triangle is equal to half the area of a rectangle with the same base 6 and altitude A; hence the area of a triangle is given by the familiar... | |
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AC.BD, etc., absolute areas. § 90. The fundamental theorem in the mensuration of plane areas is the proposition that the area of any parallelogram is equal to the area of a rectangle contained by its base and its altitude ; or the proposition, immediately... 
