This document contains a mathematics worksheet on polygons, circles, and solving word problems involving geometric shapes and measurements. There are multiple choice questions, fill-in-the-blank questions, and word problems assessing skills like identifying polygons, finding perimeters and areas, converting between measurement units, and calculating volumes and circumferences of circles. The challenges at the end require applying these concepts to solve multi-step word problems.

1. MTAP Program of
Excellence in Mathematics
Grade 5 Session 6
Name of Facilitator

2. POLYGONS

3. A. Tell whether the following figure is a polygon
or not.
P
1. 2. 3. 4. 5.
NP P P NP
P NP NP NP P
6. 7. 8. 9. 10.

4. B. Count the number sides and give the name of
the polygons.
1.
2.
3.
4.
5.
4 sides,
Quadrilateral
6 sides,
Hexagon
12 sides,
Dodecagon
8 sides,
Octagon
5 sides,
Pentagon

5. C. Complete the table below.
NAME OF THE POLYGON NO. OF SIDES
1. Quadrilateral
2. 3
3. 8
4. Decagon
5. Dodecagon
6. 9
7. Hexagon
8. Heptagon
9. 20
10. Hectagon
4
Triangle
Octagon
10
12
Nonagon
Icosagon
6
7
100

6. D. Tell whether the following is TRUE or FALSE.
1. The sides of a simple polygon do not intersect and
meet only at their endpoints.
2. Complex polygons have sides which also do not
intersect.
3. Concave polygon is a polygon that has an angle that
measures more than 180 degrees.
4. Polygons that are having the same size and shape
are called similar polygons.
5. Two polygons that are having the same shape but not
necessarily the same size are said to be congruent.
TRUE
FALSE
TRUE
FALSE
FALSE

7. D. Tell whether the following is TRUE or FALSE.
6. All sides and angles of a regular polygon are
congruent.
7. A rhombus is a regular polygon.
8. A square is an irregular polygon.
9. All squares are rectangle but not all rectangles are
squares.
10. Concave polygon is a polygon that has an angle that
measures more than 180 degrees. A circle is a closed
plane figure and is the set of all points equidistant from a
fixed point called center.
TRUE
FALSE
FALSE
TRUE
TRUE

8. E. Given the figure at the right, name the
following:
1. A diameter
2. A chord
3. Radii
4. Center
5. Points on the circle
𝑩𝑪 or 𝑪𝑩
𝑨𝑪 or 𝑪𝑨 , 𝑩𝑪
or 𝑪𝑩
𝑩𝑶 or 𝑶𝑩 , 𝑶𝑪 or
𝑪𝑶 , 𝑫𝑶 or 𝑶𝑫
O
A, B, C , D

9. F. i. Give the radius of the following of its diameter is:
1. 12 cm
2. 7 cm
3. 8 ½ cm
4. 288 mm
5. 16.88 in
6 cm
3.5 cm
4 1/4 cm
144 mm
8.44 in
REMEMBER:
Radius = ½ (Diameter)

10. F. ii. Give the diameter of the following of its radius is:
1. 10 cm
2. 9 cm
3. 10.5 in
4. 10 ¾ dm
5. 6.33 m
20 cm
18 cm
21 in
21 ½ dm
12.66 m
REMEMBER:
Diameter = 2(Radius)

11. MEASUREMENTS
.

12. G. Convert the following measure to its desired units.
1. 20 cm = ______ cm 6 . 5 m2 = _______ cm2
2. 12 cm = ______ cm 7. 10 m2 = ________ cm2
3. 12.34 cm = _______ m 8. 8, 000, 000 cm2 = ______ m2
4. 8, 590 cm = ______ m 9. 5, 500 cm2 = ______ m2
5. 96.35 m = ______ cm 10. 16.05 m2 = _________ cm2
2000
1200
0.1234
85.9
9 635
50 000
100 000
800
0.55
160 500

13. H. Convert the following measure to its desired units.
1. 4 m3 = ____________ cm3 6 . 6 L m2 = ________ cm3
2. 0.7 m3 = __________ cm3 7. 1, 500 L m2 = _______ m3
3. 3, 000, 000 cm = ______ m3 8. 250 Lcm2 = _______ m3
4. 700, 000 cm = ________ m3 9. 2, 000, 000 cm3 = ______ L
5. 2.5 L = ________ cm3 10. 28 m3 = _______ L
4, 000,000
700, 000
3
7
2 500
6000
1.5
0.25
2000
28 000

14. SOLVING WORD
PROBLEMS

15. I. Answer each of the following problems:
1. Find the perimeter and area of a square of side:
a. 11 m b. 23 dm c. 45 cm
Answer:
a. s = 11 m : P = 4 x 11 = 44 m ; A = 11 x 11 = 121 m2.
b. s = 23 dm : P = 4 x 23 = 92 dm ; A = 23 x 23 = 529 dm2
c. s = 45 cm : P = 4 x 45 = 180 cm ; A = 45 x 45 = 2025 cm2

16. 2. Find the perimeter and area of a rectangle if:
a. L = 18 cm, W = 12 cm b. L = 2.5 m, W = 3.8 m
Answer:
a. L = 18 cm, W = 12 cm : P = 2(18 + 12) = 60 cm ;
A = 18 x 12 = 216 cm2
b. L = 2.5 m, W = 3.8 m : P = 2 (2.5 + 3.8) = 12.6 m;
A = 2.5 x 3.8 = 9.5 m2

17. 3. Vince wants to put a ribbon around the circular can of biscuits. If the
can has a radius of 24 cm, find the circumference of the can.
Answer:
r = 24 cm , C = 2πr , then C = 2(3.14)(24) = 150.72 cm. Therefore,
the circumference is 150.72 cm

18. 4. Zoie wants to sew lace along the edges of her 5 placemats. If a
placemat is 13 cm long and 9 cm wide, how many meters of lace does
she need?
Answer:
l = 13 cm, w = 9 cm ; P = 2(13+9) = 44 cm lace needed for one
placemat, since Zoie has 5 placemats, so 5(44cm) = 220 cm.
The total length of lace needed in meters is 2.2.

19. 5. John’s father built a wading pool for him that is 2.5 meters by 3.5
meters. If John walks around the pool 7 times, how many meters will
that be?
Answer:
l = 2.5 m, w=3.5 m ; P = 2(2.5+3.5)m = 12 m. If John walks
around 7 times, then that would be 7 x 12 = 84 m.

20. 6. Jhumar wants to tie a rope around a post that has a circular cross
section of 1.5 m. What is the circumference around it?
Answer:
d = 1.5 m ; C = 2πr, then C = 2(3.14)(1.5) = 9.42 m.
Then the circumference of the post is 9.42 m.

21. 7. The distance around the circular field is 471meters.
a. Find the diameter of the circular field.
b. What is the area of the circular field?
The distance around the circular field is 471 meters.
a. C = πd, 471 = (3.14)(d), 471÷3.14 = d, d = 150 m
Answer:
b. d = 150 m, so r = 75 m;
A = πr2 , then A = (3.14)(75m)2 = 17, 662.5 m2

22. 8. A rectangular prism has a height of 3 in, width of 3 in and length of
8 in. Find the volume of the rectangular prism.
Answer:
l = 8 in, w = 3 in, and h = 3 in :V = lwh , then V = 8(3)(3)in3 = 72 in3.
Therefore, the volume of the rectangular prism is 72 in3

23. 9. A square tile of side 25cm costs ₱30.50. How much would it cost to
tile the floor of a bathroom that is 5 m in length and 3 m in width?
If the tiles are squares of side 25 cm, the 5 m side needs 500/25 = 20
tiles and the 3 m side needs 300 cm/25 cm = 12 tiles.
The bathroom needs 20 rows of 12 times or 240 tiles in all.
At ₱30.50 a tile, it will cost 240 x ₱30.50 = ₱7 320.00 for the cost of
the tiles.
Answer:

24. 10. A can of sardines has a radius of 10 cm and a height of 8 cm. A
can of pineapple juice has a radius of 8 cm and a height of 10 cm.
Which cylinder has a greater volume?
V of the sardines is 3.14(10 x 10)(8) cm3 = 2 512 cm3 , while the V of
the can of pineapple juice is 3.14(8 x 8)10 cm3 = 2 000.6 cm3.
Therefore, the can of sardines has a greater volume.
Answer:

25. CHALLENGE!

26. Let us apply what we
learned!

27. Solve the following problems.
1. Sean is going to paint a circle on a piece of cardboard. The
area of the circle is 706.5 square centimeters. What is the
radius of the circle?
1. A of the circle is 706.5 cm2, therefore 706.5 cm2 = 3.14r2, so 225 cm2
= r2, √225 = r.
Therefore r = 15 cm.

28. 2. The circumference of a circular clock is 244.92 dm. What is
the diameter of the clock? Find the area of the clock.
The circumference of a circular clock is 244.92 dm.
a. What is the diameter of the clock? C = πd, 244.92 = (3.14)d,
then 244.92÷3.14 = d , so d= 78 dm.
b. Find the area of the clock. A = πr2, since d = 78 dm, so r= 39
dm, computing for the area A = (3.14)(39)2, therefore A = 4
775.94 dm2

29. 3. Three cans have capacities of three, five and nine liters. How
can you use the cans to measure exactly 7 liters of water?
Three cans have capacities of 3 L, 5 L and 9 L. To get 7 L of water
using the three cans, water has to go from one can to another as
shown. The numbers show – begin with 9 L of water in the 9 L can.
Then fill the 3 L can and 5 L can. Next place the content of the 3 L can
into the 9 L can. Then, fill the 3 L can from the 5 L can. Finally, empty
the 3 L can into the 9 L can, to have 7 liters of water in it.

30. 4. To fence the side of his property facing a street, Mr. Cruz
planned to use fence posts 2 meters apart. Because of the
increase in the price of the posts, he decided to buy 4 fewer
posts and place them 3 meters apart. How many posts would
he have bought at first?
Let x be the number of posts he would have bought at first to be placed 2 m
apart. That gives x -1, 2 m spaces and the space to be fenced 2(x-1) m. If
there are 4 fewer posts, that means x – 5 spaces 3 m apart and 2(x – 1) m =
3(x – 5) m.
Solving gives 2(x -1)m = 3(x – 5) m. 2x – 2 = 3x – 15. x = 13 posts to be
bought at first to fence 12 x 2 m = 24 m. Buying 4 posts fewer means
buying only 9 and the same space 3 x 8 = 24 m can be fenced.

31. 5. A swimming pool that is 25 m by 15 m has a 2 m concrete walk
built around it. What is the area of the pool and walk? What is the
area of the walk?
The swimming pool has an area of 25 x 15 = 375 sq. m. The area of the pool
and concrete walk is 29 x 19 sq.m. = 551 sq. m. Area of walk = (551 – 375)
sq.m. = 176 sq.m.
m
2

m
25
m
27

32. 6. If one box is 1 cubic centimeter, what is the volume of this
figure?
If one box is 1 cubic centimeter, then;
V of the figure = V1 + V2 + V3 + V4 + V5
= 16 cm3 + 12 cm3 + 8 cm3 + 4 cm3 + 2cm3
= 42 cm3