geometry and trigo

Given a circle whose diameter is AB equals to 2m. If two points C and D lie on the circle and angles ABC and BAD are 18 deg and 36 deg, find the length of the major arc CD. a. 1.26 m b. 1.36 m c. 1.63 m d. 1.45 m

1.26 m

A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border. a. 1.76 cm b. 1.35 cm c. 1.98 cm d. 2.03 cm

1.76 cm

If the sides of a parallelogram and an included are 6, 10 and 100 degrees respectively, find the length of the shorter diagonal. a. 10.63 b. 10.37 c. 10.73 d. 10.23

10.73

Find the area of the quadrilateral shown, AB=10 cm, BC = 5 cm, CD = 14.14 cm, and DA = 15 cm, if the sum of the opposite angles is equal to 225 degrees a. 96 sq. cm b. 100 sq. cm c. 94 sq. cm. d. 98 sq. cm.

100 sq. cm

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side 10 cm long? a. 104.7 b. 105.7 c. 106.7 d. 107.7

104.7

The area of a circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle is sq. m? a. 100.25 b. 102.25 c. 104.25 d. 105.25

105.25

Find the area of a regular pentagon whose side is 25m and apothem is 17.2m a. 1075 m2 b. 1085 m2 c. 1080 m2 d. 1095 m2

1075 m2

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm a. 12.73 m b. 13.52 m c. 14.18 m d. 15.55 m

12.73 m

Find each interior angle of a hexagon. a. 90 deg b. 120 deg c. 150 deg d. 180 deg

120 deg

The arc of a sector is 9 units and its radius is 3 units. What is the area of the sector in square units. a. 12.5 b. 13.5 c. 14.5 d. 15.5

13.5

The area of a triangle inscribed in a circle is 39.19 cm2 and the radius of the circumscribed circle is 7. 14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side. a. 11 cm b. 12 cm c. 13 cm d. 14 cm

14 cm

A square section ABCD has one of its side equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED. a. 130 deg b. 140 deg c. 150 deg d. 160 deg

150 deg

Each angle of a regular dodecagon is equal to. a. 135 deg b. 150 deg c. 125 deg d. 105 deg

150 deg

A trapezoid has an area of 36 m2 and an altitude of 2m. Its two bases have ratio of 4:5. What are the length of the bases. a. 12, 15 b. 7, 11 c. 8, 10 d. 16, 20

16, 20

Find the area of a quadrilateral have sides 12m, 20m, 8m, and 16.97m. if the sum of the opposite angles is equal to 225 degrees. Find the area of the quadrilateral. a. 100 m2 b. 124 m2 c. 168 m2 d. 158 m2

168 m2

How many diagonals are there in a polygon of 20 sides? a. 200 b. 170 c. 100 d. 158

170

Find the difference of the area of the square inscribed in a semi-circle having a radius of 15m. The base of the square lies on the diameter of the semi-circle. a. 171.5 cm2 b. 172.5 cm2 c. 173.5 cm2 d. 174.5 cm2

173.5 cm2

The angle subtended by an arc is 24 deg. if the radius of the circle is 45 cm. Find the length of the arc. a. 16.85 cm b. 17.85 cm c. 18.85 cm d. 19.85 cm

18.85

Find the sum of the interior angles of the vertices of a five-pointed star inscribed in a circle. a. 150 deg b. 160 deg c. 170 deg d. 180 deg

180 deg

The area of a triangle is 8346 sq. m and two of its interior angles are 37'25 and 56'17. What is the length of the longest side. a. 171.5 m b. 181.5 m c. 191.5 m d. 200.5 m

181.5 m

From a point outside of an equilateral triangle, the distance to the vertices are 10 m, 18 m and 10 m. What is the length of one side of a triangle. a. 17.75 m b. 18.50 m c. 19.95 m d. 20.50 m

19.95 m

Find the angle in mils subtended by a line 10 yards long at a distance of 5000 yards. a. 1 b. 2 c. 2.5 d. 4

2

The sides of a triangle are 8cm, 10 cm and 14 cm. Determine the radius of the inscribed circle. a. 2.25 cm b. 2.35 cm c. 2.45 cm d. 2.55 cm

2.45 cm

The area of a regular hexagon inscribed in a circle of radius 1 is a. 1.316 b. 2.945 c. 2.598 d. 3.816

2.598

A rectangle ABCD which measures 18 cm by 24 cm is folded once, perpendicular to diagonal AC, so that the opposite vertices coincide. Find the length of the fold. a. 20.5 cm b. 21.5 cm c. 22.5 cm d. 23.5 cm

22.5 cm

How many sides are in a polygon if each interior angle is 165 deg? a. 12 b. 24 c. 20 d. 48

24

Given a triangle, C = 100 deg, a = 15m, b = 20m. Find c a. 26 m b. 27 m c. 28 m d. 29 m

27 m

Determine the area of the quadrilateral shown, OB=80 cm, AO = 120 cm, OD = 150 cm, and theta = 25 degrees a. 2721.66 cm2 b. 2271.66 cm2 c. 2172.66 cm2 d. 2217.66 cm2

2721.66 cm2

Find the area (in cm2) of a regular octagon inscribed in a circle of radius 10 cm. a. 283 b. 289 c. 298 d. 238

283

In triangle ABC, angle A = 45 deg, C = 70 deg. The side opposite angle C is 40 m long. What is the length of the side opposite angle A. a. 26.1 m b. 27.1 m c. 29.1 m d. 30.1 m

30.1 m

Two perpendicular chords 5cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part. a. 30 cm2 b. 31 cm2 c. 32 cm2 d. 33 cm2

31 cm2

A rhombus has diagonals of 32 and 20 inches. Determine its area. a. 360 in2 b. 280 in2 c. 320 in2 d. 400 in2

320 in2

The area of a circle is 89.42 sq. inches. What is its circumference? a. 32.25 in b. 33.52 in c. 35.33 in d. 35.55 in

33.52 in

Assuming that the earth is a sphere whose radius is 6400 km. Find the distance along a 3-degree arc at the equator of the earth's surface. a. 335.10 km b. 533.10 km c. 353.10 km d. 353.01 km

335.10 km

In triangle ABC, angle C = 70 deg, A = 45 deg, AB = 40 m. What is the length of the median drawn from the vertex A to side BC? a. 36.3 m b. 36.6 m c. 36.9 m d. 37.2 m

36.3 m

A circle having an area of 452 sq. m is cut into two segments by a chord which is 6m from the center of the circle. Compute the area of the bigger segment. a. 354.89 sq. m b. 363.68 sq. m c. 378.42 sq. m d. 383.64 sq. m

363.68 sq. m

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 9m and each circle passes through the center of the other. Find the area of the swimming pool. a. 380 m2 b. 390 m2 c. 400 m2 d. 410 m2

410 m2

The sum of the interior angles of a polygon is 540 deg. Find the number of sides. a. 3 b. 4 c. 5 d. 6

5

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle? a. 5.533 in b. 5.335 in c. 6.335 in d. 7.335 in

5.335 in

In a circle of diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the area of that part not covered by the star? a. 40.5 sq. m b. 45.5 sq. m. c. 50.5 sq. m d. 55.5 sq.m

50.5 sq. m

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon. a. 430.70 cm3 b. 573.26 cm3 c. 473.77 cm3 d. 516.14 cm3

516.14 cm3

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides. a. 441.66 cm2 b. 467.64 cm2 c. 519.60 cm2 d. 493.62 cm2

519.60 cm2

A regular hexagon is inscribed in a circle whose diameter is 20m. Find the area of the 6 segments of the circle formed by the sides of the hexagon. a. 36.45 sq.m b. 63.54 sq.m c. 45.63 sq.m d. 54.36 sq.m

54.36 sq.m

The angle of a sector is 30 degrees, and the radius is 15 cm, what is the area of the sector is cm2. a. 59.8 b. 89.5 c. 58.9 d. 85.9

58.9

The distance between the centers of three circles which are mutually tangent to each other externally are 10, 12 and 14 units. The area of the largest circle is. a. 72 pie b. 23 pie c. 64 pie d. 16 pie

64 pie

A certain angle has a supplement 5 times its complement. What is the angle? a. 67.5 deg b. 58.5 deg c. 30 deg d. 27 deg

67.5 deg

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the circumscribing circle. a. 7.14 cm b. 7.34 cm c. 7.54 cm d. 7.74 cm

7.14 cm

How many sides has a polygon if the sum of the interior angles is 1080 deg. a. 5 b. 6 c. 7 d. 8

8

Two sides of a triangle are 50 m and 60 m long. The angle included between this sides is 30 deg. What is the interior angle opposite the longest side? a. 93.74 deg b. 92.74 deg c. 90.74 deg d. 86.38 deg

86.38 deg

A rat fell on a bucket of a water wheel with a diameter of 600 cm which traveled an angle of 190 deg before it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell. a. 950 b. 965 c. 985 d. 995

995