(iii) What valu creases? Explain. 20. Prove Theorem 4.3.1 for the case where point D lies between points 21. Redraw Fig. 4.3.2 so that A is between E and D and then prove 22. Use Heron's formula (see the Historical Note at the beginning of this E and F (see Fig. 4.3.2). Theorem 4.3.1. section) to determine the area of the triangle shown in Fig. 4.3.4. 26 Note: In Exercises 23-26, you may use the Pythagorean relationship (i.e. a2+b2=c2) even though this result won't be proved until the next section 23. If A ABC is a 3 cm-4 cm-5 cm right triangle with the right angle at C. show that Heron's formula gives the same area as Theorem 4.3.4 24. If A ABC is a right triangle with legs of length a and b and with hypotenuse of length c, show that Heron's formula gives the same area as Theorem 4.3.4. 25. Show an equilateral triangle in which each side has length s has area 4.4 HIST the r tribu given by A - 3 alge the Figure 4.3.3 The elementary theorems listed next are derived in a similar fashion the proofs are left as exercises. Some theorems involve the use of terms he are familiar but have not yet been defined (e.g., the height of a triangle), As you consider these theorems, try to formulate valid definitions for the vocah. ulary used. Several of the exercises involve writing these definitions. Theorem 4.3.3. The area ofa right triangle is one-half the product of the lengths of its legs. Theorem 4.3.4. The area of a triangle is one-half the product of any base and the corresponding height. Theorem 4.3.5. The area of a trapezoid is the product of its height and the arithmetic mean of its bases. Theorem 4.3.6 The area of a rhombus is one-half the product of the lengths of the diagonals. In addition, several other standard area formulas concerning polygonal regions are explored as exercises in the following set.
(iii) What valu creases? Explain. 20. Prove Theorem 4.3.1 for the case where point D lies between points 21. Redraw Fig. 4.3.2 so that A is between E and D and then prove 22. Use Heron's formula (see the Historical Note at the beginning of this E and F (see Fig. 4.3.2). Theorem 4.3.1. section) to determine the area of the triangle shown in Fig. 4.3.4. 26 Note: In Exercises 23-26, you may use the Pythagorean relationship (i.e. a2+b2=c2) even though this result won't be proved until the next section 23. If A ABC is a 3 cm-4 cm-5 cm right triangle with the right angle at C. show that Heron's formula gives the same area as Theorem 4.3.4 24. If A ABC is a right triangle with legs of length a and b and with hypotenuse of length c, show that Heron's formula gives the same area as Theorem 4.3.4. 25. Show an equilateral triangle in which each side has length s has area 4.4 HIST the r tribu given by A - 3 alge the Figure 4.3.3 The elementary theorems listed next are derived in a similar fashion the proofs are left as exercises. Some theorems involve the use of terms he are familiar but have not yet been defined (e.g., the height of a triangle), As you consider these theorems, try to formulate valid definitions for the vocah. ulary used. Several of the exercises involve writing these definitions. Theorem 4.3.3. The area ofa right triangle is one-half the product of the lengths of its legs. Theorem 4.3.4. The area of a triangle is one-half the product of any base and the corresponding height. Theorem 4.3.5. The area of a trapezoid is the product of its height and the arithmetic mean of its bases. Theorem 4.3.6 The area of a rhombus is one-half the product of the lengths of the diagonals. In addition, several other standard area formulas concerning polygonal regions are explored as exercises in the following set.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
24
Transcribed Image Text:(iii) What valu
creases? Explain.
20. Prove Theorem 4.3.1 for the case where point D lies between points
21. Redraw Fig. 4.3.2 so that A is between E and D and then prove
22. Use Heron's formula (see the Historical Note at the beginning of this
E and F (see Fig. 4.3.2).
Theorem 4.3.1.
section) to determine the area of the triangle shown in Fig. 4.3.4.
26
Note: In Exercises 23-26, you may use the Pythagorean relationship (i.e.
a2+b2=c2) even though this result won't be proved until the next section
23. If A ABC is a 3 cm-4 cm-5 cm right triangle with the right angle at
C. show that Heron's formula gives the same area as Theorem 4.3.4
24. If A ABC is a right triangle with legs of length a and b and with
hypotenuse of length c, show that Heron's formula gives the same
area as Theorem 4.3.4.
25. Show an equilateral triangle in which each side has length s has area
4.4
HIST
the r
tribu
given by A - 3
alge
the
Transcribed Image Text:Figure 4.3.3
The elementary theorems listed next are derived in a similar fashion
the proofs are left as exercises. Some theorems involve the use of terms he
are familiar but have not yet been defined (e.g., the height of a triangle), As
you consider these theorems, try to formulate valid definitions for the vocah.
ulary used. Several of the exercises involve writing these definitions.
Theorem 4.3.3. The area ofa right triangle is one-half the product of the
lengths of its legs.
Theorem 4.3.4. The area of a triangle is one-half the product of any base
and the corresponding height.
Theorem 4.3.5. The area of a trapezoid is the product of its height and the
arithmetic mean of its bases.
Theorem 4.3.6 The area of a rhombus is one-half the product of the lengths
of the diagonals.
In addition, several other standard area formulas concerning polygonal
regions are explored as exercises in the following set.
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