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Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu.

During the festival of Onam , your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure.

Design II: This Pookalam is made with 9 circular design each of radius 7cm.

Refer Design I:

1. The side of equilateral triangle is

a) 12√3 cm

b) 32√3 cm

c) 48cm

d) 64cm

2. The altitude of the equilateral triangle is

a) 8 cm

b) 12 cm

c) 48cm

d) 52cm

Refer Design II:

3. The area of square is

a) 1264 cm2

b) 1764 cm2

c) 1830 cm2

d) 1944 cm2

4. Area of each circular design is

a) 124 cm2

b) 132 cm2

c) 144 cm2

d) 154 cm2

5. Area of the remaining portion of the square ABCD is

a) 378 cm2

b) 260 cm2

c) 340 cm2

d) 278 cm2

2 Answers

+1 vote
by (46.5k points)
selected by
 
Best answer

1. b) 32√3 cm

Let centre of circle be O.

Join OA, OB and OC

Now,

OA = OB = OC = Radius of circle = 32 cm

Let's consider △OBC

Let' s draw OM⊥BC

By Symmetry

BM = CM = 1/2 BC

∠ BOM = ∠ COM = 1/2 x 120° = 60°

In right triangle △OMB

Thus,

2. c) 48 cm

Altitude of equilateral triangle

= AM

= OA + OM

= 32 + OM

Let's Find OM

Let's take △OMB

In right triangle △OMB

Thus,

Altitude of equilateral triangle = 32 + OM = 32 + 16 = 48 cm

3. b) 1764 cm2

Now,

Area of square = (side)2

= (42)2

= 1764 cm2

4. d) 154 cm2

Circular Design is circle with radius 7 cm

5. a) 378 cm2

Area of remaining portion 

= Area of square - Area of 9 circles

= Area of square - 9x Area of 1 circle

= 1764-9 × 154

= 1764 - 1386

= 378 cm2

+2 votes
by (28.9k points)

1. b) 32√3 cm

2. c) 48 cm

3. b) 1764 cm2

4. d) 154 cm2

5. a) 378 cm2

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