Compilation of Problems in Geometry |

**COMPILATION OF MATH PROBLEMS**

**SOLID MENSURATION**

1.Determine the value of each interior angle of a regular dodecagon.

2.How many sides has a polygon if the sum of the interior angles is 2520° ?

3.How many sides has polygon if the sum of its interior angles equals the sum of its exterior angles?

4.How many diagonals are there in a hexagon?

5.The area of a circle circumscribing a regular octagon is 100π. Find the area of the octagon.

6.Find the area of a pentagon whose apothem is 10 cm.

7.Determine the area of a regular 6-point star polygon if the inner regular hexagon has 10 cm side.

8.One side of a parallelogram is 10 cm and its diagonals are 16 cm and 24 cm, respectively. Find its area.

9.A piece of wire is shaped to enclose a square whose area is 169 in^2. It is then reshaped to form a rectangle whose length is 15 in. Determine the area of the rectangle.

10.A rhombus has an area of 320 cm^2. If one diagonal measures 20 cm, determine the length of each side.

11.Find the area of a circle inscribed in a rhombus whose perimeter is 100 cm and whose longer diagonal is 40 cm.

12.Find the area of an isosceles trapezoid if the measure of one angle is 135° and the lengths of the bases are 10 and 18.

13.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.

14.In a circle whose radius is 12, find the area of a minor segment whose arc has a central angle of 60° .

15.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.

16.What is the surface area of a cube whose space diagonal is 6.

17.A parallelepiped has an altitude of 20 inches. The base is a parallelogram with adjacent sides 8 inches and 12 inches and included angle 60°. Find its volume.

18.The base of a pyramid is a regular hexagon with each side equal to 6 m and an altitude of 10 m. What is the volume of water it can hold when full and inverted?

19.The lateral area of the right circular water tank is 92 sq. cm. Its volume is 342 cu. m., determine its radius.

20.Determine the volume of a right circular cone of radius 8 cm and slant height of 17 cm.

21.The frustum of a pyramid has a lower base 50 m by 10 m and an upper base of 40 m by 8 m. If the altitude of the frustum is 6 m, determine its volume.

22.Determine the total surface of an icosahedron if the length of each edge is 5 inches.

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