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reaY eht fo naicitamehtaM > Plane Geometry > Flashcards

Plane Geometry Flashcards

1
Q

Set 1 Problem 2: How many sides does a polygon have if the sum of the interior angles is three times as large as the sum of the exterior angles?

A

8 (p. 7)

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2
Q

Set 1 Problem 5: Find the area of a square inscribed in a circle with radius 8 cm.

A

128 cm² (p. 8)

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3
Q

Set 1 Problem 8: Two squares with sides 15 cm overlap each other so that the overlapping area forms a regular octagon. Find the overlapping area

A

186.30 cm² (p. 8)

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4
Q

Set 1 Problem 11: Find the perimeter of a regular hexagon whose apothem is 15 cm.

A

103.92 cm (p. 9)

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5
Q

Set 1 Problem 19: A parallelogram has diagonals 22 cm and 28 cm, and one side measures 10 cm. Find the area of the parallelogram.

A

218.59 cm² (p.10)

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6
Q

Set 2 Problem 32: What is the measure of an interior angle of a regular dodecagon?

A

150°

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7
Q

Set 2 Problem 37: Given the four sides of a quadrilateral: a=12 cm, b=16 cm, c=18 cm, and d=14 cm. The sum of the opposite angles B and D is 120°. Compute the area of the quadrilateral.

A

190.49 cm² (p.29)

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8
Q

Set 2 Problem 38: Find the area of a sector of a circle with radius 32 cm and central angle of 1.2 radians.

A

614.40 cm² (p.29)

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9
Q

Set 2 Problem 40: Find the area of a cyclic quadrilateral whose sides are 5 cm, 7 cm, 10 cm, and 16 cm.

A

67.35 cm²

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10
Q

Set 2 Problem 65: The area of a regular hexagon is 300 square units. Find its apothem.

A

9.3 (p.33)

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11
Q

Set 3 Problem 24: At the entrance of a racetrack a flag is located. Another flag is located inside the track and at a distance of half a mile from the first. A jockey notes that no matter where he is on the track, one flag is 3 times as far away as the other. How long is the track, in ft?

A

1,980π ft (p.45)

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12
Q

Set 3 Problem 48: A lot in the form of quadrilateral is situated on the corner of 2 streets intersecting at an angle of 78°. On one street, the side is 134.28 m and on the other street, the side is 106.74 m. The other two sides are perpendicular to each side of the street. Compute the area of the lot.

A

11,524.74 m^2 (p.50)

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13
Q

Set 3 Problem 54: A trapezoidal piece of land has parallel sides 438 m and 576 m respectively. The non-parallel sides are 290 m and 354 m. This lot is to be divided into 2 parts in the ratio 2:3 by a line parallel to the parallel sides, the larger part to be adjacent to the smaller parallel side. Compute the length of the dividing line.

A

525.17 m (p.51)

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14
Q

Set 4 Problem 13: Find the radius of the circle circumscribing an equilateral triangle with sides 20 cm?

A

11.547 (p.61)

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15
Q

A point within a equilateral triangle has distances of 3 m, 4 m, and 5 m respectively from the vertices.
Set 4 Problem 51: Determine the perimeter of the triangle.

A

20.30 m (p.67)

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16
Q

A point within a equilateral triangle has distances of 3 m, 4 m, and 5 m respectively from the vertices.
Set 4 Problem 52: Determine the radius of the circle escribed outside the triangle which is tangent to one of the sides.

A

5.86 m (p.68)

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17
Q

A point within a equilateral triangle has distances of 3 m, 4 m, and 5 m respectively from the vertices.
Set 4 Problem 53: Compute the distance from the circumcenter of the circle to one of the sides.

A

1.95 m (p.68)

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18
Q

Set 4 Problem 74: A tangent and a secant are drawn to a circle from the same external point. If the internal segment of the secant is 6 units and the tangent is 8 units long to the point of tangency, determine the length of the secant.

A

11.44 units (p. 72)

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19
Q

Set 4 Problem 74: A tangent and a secant are drawn to a circle from the same external point. If the internal segment of the secant is 6 units and the tangent is 8 units long to the point of tangency, determine the length of the secant.

A

11,384,955 ft^2 (p. 72)

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20
Q

Set 4 Problem 75: A recreation park planned to be constructed consisting of 2 roads tangents to a circular arc which is concave towards the point of intersection of two tangent roads. Each tangent road and the arc of the circle is mile long and the boundaries of the park. Compute the area of the park.

A

11,384,955 ft^2 (p. 72)

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21
Q

Set 5 Problem 18: Two square lots of unequal sizes lie adjacent to each other. Together the 2 lots contain contain an area of 6568 m^2. To enclose them in a single enclosure, it would require 356 m of fence. Find the distance of the smaller lot.

A

22 m x 22 m (p.80)

22
Q

Set 5 Problem 58: Find the area of a regular octagon inscribed in a circle of radius 5 cm.

A

70.71 cm^2 (p.86)

23
Q

Set 5 Problem 61: An isosceles trapezoid will have 2 diagonals AC and BD. Given that AC=5x+13 and BD=11x-5, the length of the diagonal is nearest to

A

28 (p.86)

24
Q

Set 6 Problem 10: The bases of an isosceles trapezoid measure 10 cm and 18 cm respectively. Find the area of this isosceles trapezoid if one angle measures 135°.

A

56 cm^2 (p.95)

25
Q

A cyclic quadrilateral has sides AB=5.56 cm, BC=7.18 cm, CD=2.68 cm, and CA=4.83 cm.
Set 6 Problem 26: Find the length of the diagonal AC.

A

6.58 cm (p.97)

26
Q

A cyclic quadrilateral has sides AB=5.56 cm, BC=7.18 cm, CD=2.68 cm, and CA=4.83 cm.
Set 6 Problem 27: Find the area of the quadrilateral.

A

23.02 cm^2 (p.98)

27
Q

A cyclic quadrilateral has sides AB=5.56 cm, BC=7.18 cm, CD=2.68 cm, and CA=4.83 cm.
Set 6 Problem 28: Find the radius of the inscribed circle.

A

3.77 cm (p.98)

28
Q

Set 6 Problem 46: A circle with a radius 6 cm is cut into 2 segments by a chord 8 cm long. Find the area of the smaller segment.

A

8.37 cm^2 (p.101)

29
Q

Set 6 Problem 47: A triangle is inscribed in a circle with a radius of 4 cm. If two sides of the triangle measure 3 cm and 8 cm, what is the area of the triangle?

A

13.86 cm^2 (p.101)

30
Q

Set 6 Problem 64: What is the maximum area of a triangle inscribed in a semicircle with radius 12 cm if the hypotenuse of the triangle is on the diameter of the circle?

A

108.54 cm² (p.104)

31
Q

Set 6 Problem 70: A sector of a circle AOB has a radius “r” and a central angle of 45° at O, the center of the circle, with AB as the arc. A line is drawn from point A to point X, where X is the midpoint of OB. If the area of section ABX is 4.5 cm², compute the radius of the circle, “r”.

A

5 cm (p.105)

32
Q

Set 6 Problem 71: The centers of each two spheres having equal radii of 3 m lie on the surface of each other. Find the volume common to the two spheres.

A

36.34 cm^3 (p.105)

33
Q

Set 6 Problem 32: The perimeter of a rectangular lot is 136 m and its diagonal is 52 m. Compute its area.

A

960 m^2 (p.116)

34
Q

Set 7 Problem 36: A square OPQR has sides 12 cm each. Four congruent isosceles triangles with sides equal to “x” are cut one from each corner so that the remaining portion forms a rectangular octagon. What is the value of x?

A

3.51 cm (p.116)

35
Q

Set 7 Problem 56: Two chords of a circle AB and CD intersect at point E. If it is known that EB=12 cm, EA=8 cm, and EC=6 cm, compute the length of chord CD.

A

22 cm (p.120)

36
Q

Set 7 Problem 61: Given a regular pentagon of sides 15 cm. Compute the difference in areas between the circumscribed circle and the inscribed circle of the pentagon.

A

176.92 cm² (p.121)

37
Q

Set 7 Problem 70: Two tangents are drawn to a circle from an external point P and intersect the circle at points Q and R. The angle between the tangents is 42°. Point S is a point on the circle and is nearer to P than Q and R. Find the angle QSR.

A

103° (p.122)

38
Q

Set 8 Problem 29: A triangle has sides 10 cm, 18 cm, and 20 cm. Compute the radius of the inscribed circle.

A

3.74 cm (p.133)

39
Q

A triangle ABC has sides AB=12 cm, BC=15 cm, and AC=21 cm.
Set 8 Problem 46: Find the area of the triangle.

A

88.18 cm² (p.135)

40
Q

A triangle ABC has sides AB=12 cm, BC=15 cm, and AC=21 cm.
Set 8 Problem 47: Find the length of the angle bisector of angle B from vertex B to the intersection of side AC.

A

8.43 cm (p.136)

41
Q

A triangle ABC has sides AB=12 cm, BC=15 cm, and AC=21 cm.
Set 8 Problem 48: Find the distance from vertex A to the incenter.

A

9.71 cm (p.136)

42
Q

Set 9 Problem 6: A circle is inscribed in an equilateral triangle with sides 12 cm each. A small circle is drawn so that it is tangent to the 2 sides of the triangle and tangent externally to the big circle. Compute the radius of the small circle.

A

1.155 cm (p.146)

43
Q

Set 9 Problem 42: A rectangular picture, each of whose dimensions is an integral number of inches, has an ordinary rectangular frame 1 inch wide. The area of the picture and the area of the frame are equal. Which can be the dimensions of the picture?

A

4inx6in (p.152)

44
Q

Set 9 Problem 54: A sector has a radius of 24 cm and a central angle of 100deg. Find the measure of the sides of the largest square inscribed in the sector.

A

15.94 cm (p.153)

45
Q

Set 9 Problem 67: A triangle has an area of 128.48 cm² with 2 interior angles 38° and 74°, respectively. Compute the perimeter of the triangle.

A

38.72 m (p.155)

46
Q

Set 10 Problem 2: One diagonal of a parallelogram is 15.6 cm. It makes angles 36°10’ and 14°30’ respectively with the sides. Find the area of the parallelogram.

A

46.49 cm^2 (p.161)

47
Q

Set 10 Problem 18: Find the radius of the circumscribed circle of a triangle whose sides are 10 cm, 18 cm, and 20 cm.

A

1,701 (p.165)

48
Q

Set 10 Problem 26: Two circles have radii 3 inches and 8 inches. The distance between their centers is 18 inches. How long is the common internal tangent segment between their points of tangency?

A

14.25 in (p.166)

49
Q

Set 10 Problem 27: A circle has a diameter of 30 cm. Five smaller circles are to be arranged such that they are tangent externally and their centers on the circumference of the big circle. Find the radius of each five smaller circles.

A

17.63 cm (p.166)

50
Q

Set 10 Problem 29: The apothem of a regular polygon is 6 and its perimeter is 144. The area of the polygon is

A

432 (p.167)

51
Q

Set 10 Problem 34: A chord of a circle is 10 inches long and it subtends an arc 12 inches long. Find the central angle which subtends the chord, in degrees.

A

119.6deg or 2.087 rad (p.167)

reaY eht fo naicitamehtaM (26 decks)

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