Solid Mensuration Practice Problems

SOLID MENSURATION
I. IDENTIFICATION:
_______________________1. is the art of determining the length of a line segment, area of
surfaces and volume of solid bodies.
_______________________2. is a surface such that a straight line joining any two points
in it lies wholly in the surface.
_______________________3. is any closed figure bounded by line segments
_______________________4. is a polygon having equal sides and equal angles.
_______________________5. a polygon having each side tangent to a given circle.
_______________________6. a polygon having with its vertices on the circumference of
the circle.
_______________________7. is a four - sided polygon.
_______________________8. is a quadrilateral with opposite sides parallel. The altitude
of a is the perpendicular distance between either pair of
opposite sides.
_______________________9. is a parallelogram whose four sides are equal. The diagonals
of are perpendicular to each other.
_______________________10. is a parallelogram whose adjacent sides are perpendicular
to each other so that if we call one side a base, then the other
side is an altitude. The base and altitude are often referred
to as the width and length or the dimensions.
_______________________11. is a rectangle with four sides is equal.
_______________________12. is a quadrilateral with one pair of opposite sides parallel
and the other pair is non parallel. The parallel sides are the
bases and the non parallel sides are called the legs. The
altitude is the perpendicular distance between the bases
while the line connecting the midpoints of the two legs is the
median.
_______________________13. a trapezoid whose legs are equal
_______________________14. a trapezoid whose one leg perpendicular to the base.
_______________________15. is a plane figure bounded by a closed curve called the
circumference and a portion of it is called an arc.
_______________________16. is the figure bounded by two radii and either of the arc
intercepts by those radii.
_______________________17. is a straight line terminated by two points on the
circumference.
_______________________18. is the longest chord and half of it is the radius.
_______________________19. the figure bounded by a chord and either of the arcs
subtended by that chord.
II. GIVE THE SIDE DESCRIPTION OF THE FOLLOWING POLYGON.
NUMBER NUMBER
OF SIDE DESCRIPTION OF SIDE DESCRIPTION
SIDES SIDES
1 31
2 32
3 33
4 34
5 35
6 36
7 37
8 38
9 39
10 40
11 41
12 42
13 43
14 44
15 45
16 46
17 47
18 48
19 49
20 50
21 60
22 70
23 80
24 90
25 100
26 1,000
27 10,000
28 100,000
29 1,000,000
30
III. PROBLEM SOLVING.
1. How many sides have an equiangular polygon if each interior angle is 120 degree? A
circle has 20 cm diameter is circumscribe on a regular hexagon.
Find:
a) Length of each side, cm c) Area of hexagon
b) Length of apothem, cm d) Area of the circle
2. A circle has 25 cm diameter is inscribed in an octagon.
Find:
a) Length of each side, cm c) Area of Octagon
b) Length of apothem, cm d) Area of the circle
3. Find each interior angle of a nonagon.
4. A hexagon has a perimeter of 36 inches.
Find:
a) Sum of interior angles d) Number of diagonals
b) Interior angle e) Area of hexagon
c) Exterior angle
5. Find the ratio of areas of Octagon and Pentagon if their perimeters are equal.
6. A string 88 inches long is shaped to form an octagon. It is desired to reshaped it into a
pentagon whose area is only one-half of the octagon. Find the length of string to be
removed.
7. A grazing park is in the shape of a regular decagon. A horse tied in the center
with a rope length of 15 cm. A person noticed that once the rope is fully
stretched, the horses touch the corners of the grazing park. Find the area that
the horse can graze outside the park.
8. A regular polygon has an interior angle of 150O. Find the number of diagonals
of this polygon.
9. A polygon has 90 diagonals and an apothem of 63 inches. Find the area of this
polygon.
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SOLID MENSURATION

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