The Essentials of Geometry
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In our eReader you can find the full English version of the book. Read The Essentials of Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Essentials of Geometry
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PROP. X. PROBLEM. 324. To express the area of a triangle in terms of its three sides. C D a B Given sides BC, CA, and AB, of A ABC, equal to a, b, and c, respectively. Required to express area ABC in terms of a, &, and c. Solution. Let (7 be an acute Z, and draw altitude AD. . 2 /-2 I 7)2 9 /7 v /^T") /'S 977\ .. C a -h ^ a x UIA (jj ^< <; Transposing, 2 a x CD = a 2 + 6 2 c 2 . ^^ a 2 + 6 2 - c 2 2a ( 273) = (AC + CD) (AC -CD) - c 2 ) (2 a& - a 2 c 2 ) 4 a 2 5)2_c2][ C 2_( a _5)2] 4 a 2 _ (a + 6 + c) (a + b - c) (c + a - b) (c - a + 6) 4 a 2 Now let a + b + c = 2 s. rr j_2s(2s-2c)(2s-2b)(2s-2 a) ~^T _ 16 s (s a) (s b) (s c) 4 a 2 AREAS OF POLYGONS. 173 ... AD = 2 ^ s ( s - a ) ( s ~ 6 ) ( s ~ c ) a . -. Area ABC = \ a x AD (?) = Vs(s a) (s 6) (s c). 325. Sch. Let it be required to find the area of a tri- angle whose sides are 13, 14, and 15. Let a = 13, b = 14, and c = 15 ; then s = (13 + 14 + 15) = 21. Whence, s a = 8, s 6 = 7, and s c = 6. Then, the area of the triangle is V21x 8 x 7 x 6 = V3 x 7 x 2 3 x 7x2x3 = V2 4 x 3 2 x 7 2 = 2 2 x 3 x 7 = 84.
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To quickly assess the difficulty of the text, read a short excerpt:
PROP. X. PROBLEM. 324. To express the area of a triangle in terms of its three sides. C D a B Given sides BC, CA, and AB, of A ABC, equal to a, b, and c, respectively. Required to express area ABC in terms of a, &, and c. Solution. Let (7 be an acute Z, and draw altitude AD. . 2 /-2 I 7)2 9 /7 v /^T") /'S 977\ .. C a -h ^ a x UIA (jj ^< <; Transposing, 2 a x CD = a 2 + 6 2 c 2 . ^^ a 2 + 6 2 - c 2 2a ( 273) = (AC + CD) (AC -CD) - c 2 ) (2 a& - a 2 c 2 ) 4 a 2 5)2_c2][ C 2_( a _5)2] 4 a 2 _ (a + 6 + c) (a + b - c) (c + a - b) (c - a + 6) 4 a 2 Now let a + b + c = 2 s. rr j_2s(2s-2c)(2s-2b)(2s-2 a) ~^T _ 16 s (s a) (s b) (s c) 4 a 2 AREAS OF POLYGONS. 173 ... AD = 2 ^ s ( s - a ) ( s ~ 6 ) ( s ~ c ) a . -. Area ABC = \ a x AD (?) = Vs(s a) (s 6) (s c). 325. Sch. Let it be required to find the area of a tri- angle whose sides are 13, 14, and 15. Let a = 13, b = 14, and c = 15 ; then s = (13 + 14 + 15) = 21. Whence, s a = 8, s 6 = 7, and s c = 6. Then, the area of the triangle is V21x 8 x 7 x 6 = V3 x 7 x 2 3 x 7x2x3 = V2 4 x 3 2 x 7 2 = 2 2 x 3 x 7 = 84.
What to read after The Essentials of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Webster Wells to read online
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