ssrs barcode font In Fig. 8-23, m B 90 , m ACB 58 , m D the result of part (a), find the length of CD. in Objective-C

Encode QR Code JIS X 0510 in Objective-C In Fig. 8-23, m B 90 , m ACB 58 , m D the result of part (a), find the length of CD.

In Fig. 8-23, m B 90 , m ACB 58 , m D the result of part (a), find the length of CD.
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60 ft. (a) Find the length of AB. (b) Using
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Tangents PA and PB are drawn to a circle from external point P. m APB nearest tenth the radius of the circle.
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Areas
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9.1 Area of a Rectangle and of a Square
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A square unit is the surface enclosed by a square whose side is 1 unit (Fig. 9-1). The area of a closed plane figure, such as a polygon, is the number of square units contained in its surface. Since a rectangle 5 units long and 4 units wide can be divided into 20 unit squares, its area is 20 square units (Fig. 9-2). The area of a rectangle equals the product of the length of its base and the length of its altitude (Fig. 9-3). Thus if b 8 in and h 3 in, then A 24 in2. The area of a square equals the square of the length of a side (Fig. 9-4). Thus if s 6, then A s2 36. It follows that the area of a square also equals one-half the square of the length of a diagonal. Since A s2 and s d / !2, A 1 d 2. 2 Note that we sometimes use the letter A for both a vertex of a figure and its area. You should have no trouble determining which is meant. The reader should feel free to use a calculator for the work in this chapter.
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Fig. 9-1
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Fig. 9-2
Fig. 9-3
Fig. 9-4
SOLVED PROBLEMS
9.1 Area of a rectangle (a) Find the area of a rectangle if the base has length 15 and the perimeter is 50. (b) Find the area of a rectangle if the altitude has length 10 and the diagonal has length 26. (c) Find the lengths of the base and altitude of a rectangle if its area is 70 and its perimeter is 34.
Solutions
See Fig. 9-5. (a) Here p 50 and b 15. Since p Hence, A bh 15(10) 150. 2b 2h, we have 50 b2 2(15) b2 2h so h 102 or b 10. 24.
(b) Here d 26 and h 10. In right ^ACD, d2 Hence, A bh 24(10) 240.
h2, so 262
CHAPTER 9 Areas
Fig. 9-5
(c) Here A 70 and p 34. Since p Since A bh, we have 70 b(17 we obtain h 10 or 7. Ans. 10 and 7, or 7 and 10.
2b 2h, we have 34 b), so b2 17b 70
2(b h) or h 17 b. 0 and b 7 or 10. Then since h
Area of a Square (a) Find the area of a square whose perimeter is 30. (b) Find the area of a square if the radius of the circumscribed circle is 10. (c) Find the side and the perimeter of a square whose area is 20. (d) Find the number of square inches in a square foot.
Solutions
(a) Since p (b) Since r 4s 30 in Fig. 9-6(a), s 2r 71. Then A 2 20. Then A s2
1 2 2d
(71)2 2
561. 4 200. 8 25.
10 in Fig. 9-6(b), d s
1 2 2 (20)
(c) In Fig. 9-6(a), A (d) A s . Since 1ft
20; hence, s
2 25. Then perimeter 1ft 12 in 12 in
4s 144 in .
12 in, 1 ft
Fig. 9-6
Area of a Parallelogram
The area of a parallelogram equals the product of the length of a side and the length of the altitude to that side. (A proof of this theorem is given in 16.) Thus in ~ABCD (Fig. 9-7), if b 10 and h 2.7, then A 10(2.7) 27.
Fig. 9-7
CHAPTER 9 Areas
SOLVED PROBLEMS
9.3 Area of a parallelogram (a) Find the area of a parallelogram if the area is represented by x2 4, the length of a side by x and the length of the altitude to that side by x 3. 4,
(b) In a parallelogram, find the length of the altitude if the area is 54 and the ratio of the altitude to the base is 2:3.
Solutions
See Fig. 9-7. (a) A x2 4, b x Hence, A x2 4 4, h x 3. Since A 64 4 60. bh or 54 bh, x2 4 (3x)(2x) (x 4)(x 3) or x2 4 x2 and x 3. x2 x 12 and x 8.
(b) Let h 2x, b 3x. Then A Hence, h 2x 2(3) 6.
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