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9.23. Find the area of isosceles trapezoid ABCD in Fig. 9-22, if (a) b (b) b (c) b 17, l 22, b 16, b 10, and h 12, and l 6 13 45 (d) b (e) b 20, l 40, b 8, and m/A 20, and m/A 60 28

(9.7)

9.24. (a) Find the length of the altitude of a trapezoid if the bases have lengths 13 and 7 and the area is 40.

(9.7)



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(b) Find the length of the altitude of a trapezoid if the sum of the lengths of the bases is twice the length of the altitude and the area is 49. (c) Find the sum of the lengths of the bases and the median of a trapezoid if the area is 63 and the altitude has length 7.

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Find the lengths of the bases of a trapezoid if the upper base has length 3 less than the lower base, the altitude has length 4, and the area is 30.





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(e) Find the lengths of the bases of a trapezoid if the lower base has length twice that of the upper base, the altitude has length 6, and the area is 45 925 In an isosceles trapezoid (a) Find the lengths of the bases if each leg has length 5, the altitude has length 3, and the area is 39 (b) Find the lengths of the bases if the altitude has length 5, each base angle measures 45 , and the area is 90 (c) Find the lengths of the bases if the area is 42 23, the altitude has length 3 23, and each base angle measures 60 (d) Find the length of each leg if the bases have lengths 24 and 32 and the area is 84.

4.1 Author, user, user agent (UA). 4.2 UA overrides user, which overrides author. 4.3 Property and value.

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(e) Find the length of each leg if the area is 300, the median has length 25, and the lower base has length 30 926 Find the area of a rhombus if (a) The diagonals have lengths 8 and 9 (b) The diagonals have lengths 11 and 7 (c) The diagonals have lengths 4 and 6 23 (d) The diagonals have lengths 3x and 8x (e) One diagonal has length 10 and a side has length 13 (f) The perimeter is 40 and a diagonal has length 12 (g) The side has length 6 and an angle measures 30 (h) The perimeter is 28 and an angle measures 45 (i) The perimeter is 32 and the length of the short diagonal equals a side in length (j) A side has length 14 and an angle measures 120 927.

Find the area of a rhombus to the nearest integer if (a) the side has length 30 and an angle measures 55 ; (b) the perimeter is 20 and an angle measures 33 ; (c) the side has length 10 and an angle measures 130 (98) 928 In a rhombus, find the length of (a) A diagonal if the other diagonal has length 7 and the area is 35 (b) The diagonals if their ratio is 4:3 and the area is 54 (c) The diagonals if the longer is twice the shorter and the area is 100 (d) The side if the area is 24 and one diagonal has length 6 (e) The side if the area is 6 and one diagonal has length 4 more than the other 929.

A rhombus is equal to a trapezoid whose lower base has length 26 and whose other three sides have length 10 Find the length of the altitude of the rhombus if its perimeter is 36 (98) (98) (98) (98) (97).

9.30. Provide the proofs requested in Fig. 9-23.

5

(9.9)

Fig. 9-23

9.31. Provide the proofs requested in Fig. 9-24.

(9.9)

Fig. 9-24

9.32. Prove each of the following: (a) A median divides a triangle into two triangles having equal areas.

(9.10)

In This :

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