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" Hence the area of a trapezoid is equal to its altitude, multiplied by the line which joins the middle points of the sides which are not parallel. "
Observational Geometry - Page 186
by William Taylor Campbell - 1899 - 240 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...triangles generally, are to each other, as the products of their bases and altitudes. THEOREM. 178. The area of a trapezoid is equal to its altitude multiplied by the half sum of its parallel bases. Let ABCD be a trapezoid, EF its altitude, AB and CD its parallel...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...generally, are to each ęther, as the products of their bases and altitudes. Vr PROPOSITION VII. THEOREM. The area of a trapezoid is equal to its altitude multiplied by the half sum of its parallel bases. Let ABCD be a trapezoid, EF its a!ti- p E tude, AB and CD its parallel...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...of the squares on AB, CB, diminished by twice the rectangle contained by AB, CB. PROP. VI. THEOREM. The area of a trapezoid is equal to its altitude multiplied by half the sum of its parallel bases. Let ABCD be the trapezoid, and EF its altitude ; we have to prove...
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Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - Geometrical drawing - 1846 - 254 pages
...x BE. AS If the base is 20, and altitude 15 feet, the area will be 300 square feet. 17. What is the area of a trapezoid ? The area of a trapezoid is equal to half the sum of its parallel sides multiplied by the perpendicular distance between them. Thus, area...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...AD (Prop. V.); hence that of the triangle must be iBC x AD, or BC x iAD. PROPOSITION VII. THEOREM. The area of a trapezoid is equal to its altitude multiplied, by the half sum of its parallel bases. I^et ABCD be a trapezoid, EF its altitude, AB and CD its parallel...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...equal to — — ; 2i hence, the area of the trapezoid may also be expressed by EFxHI] consequently, the area of a trapezoid is equal to its altitude multiplied by the line which connects the middle points of its inclined sides. PROPOSITION VIII. THEOEEM. The square...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...is also equal to ; 2t hence, the area of the trapezoid may also be expressed by EFxHI; consequently, the area of a trapezoid is equal to its altitude multiplied by the line which connects the middle points of its inclined sides. PROPOSITION VIII. THEOREM. The square...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1860 - 246 pages
...AK is equal to DK. Now, since KF is equal to AG, the area of the trapezoid is equal to DE xKF. Hence the area of a trapezoid is equal to its altitude, multiplied by the line which joins the middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...is equal to DK. Now, since KF is equal to AG, the area of the trapezoid is equal to DE x KF. Hence the area of a trapezoid is equal to its altitude multiplied by the line which joins the middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1885 - 540 pages
...are equal in all respects, LB = CK ; hence, AL + DK = AB + DC ; and we have HI = ^ (AB + DC) : hence, The area of a trapezoid is equal to its altitude multiplied by the line which connects the middle points of its inclined sides. -^ PROPOSITION VIII. THEOREM. Let...
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