851. Each side of an equilateral triangle is 6 cm. Find its area.
     

1. 1. 9√3 sq.cm.
      

   
   
   

   2. 6√3 sq.cm.
      

   
   
   

   3. 4√3 sq.cm.
      

   
   
   

   4. 8√3 sq.cm.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 6, Area of the equilateral triangle =
   

   √3	× (side)²
   4

   
   

   =	√3	× 6 × 6 = 9√3 sq.cm.
   	4

   Correct Option: A

   Using Rule 6, Area of the equilateral triangle =
   

   √3	× (side)²
   4

   
   

   =	√3	× 6 × 6 = 9√3 sq.cm.
   	4

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852. If a triangle with base 8 cm has the same area as a circle with radius 8 cm, then the corresponding altitude (in cm) of the triangle is
     

1. 1. 12π
      

   
   
   

   2. 20π
      

   
   
   

   3. 16π
      

   
   
   

   4. 32π

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1 and 14,
   Let the corresponding altitude of the triangle = x cm.
   According to the question, Area of the triangle = Area of the circle
   

   ⇒	1	x × 8 = π × 8 × 8
   	2

   
   ⇒ x = 2 × 8 π = 16π cm.

   Correct Option: C

   Using Rule 1 and 14,
   Let the corresponding altitude of the triangle = x cm.
   According to the question, Area of the triangle = Area of the circle
   

   ⇒	1	x × 8 = π × 8 × 8
   	2

   
   ⇒ x = 2 × 8 π = 16π cm.

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853. The measures (in cm) of sides of a right angled triangle are given by consecutive integers. Its area (in cm²) is
     

1. 1. 9
      

   
   
   

   2. 8
      

   
   
   

   3. 5
      

   
   
   

   4. 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   3² + 4² = 5²
   ∴ Base = 3 cm and
   perpendicular = 4 cm
   ∴ Area of the right angled triangle
   

   =	1	× base × height
   	2

   
   

   =	1	× 3 × 4 = 6 sq.cm.
   	2

   Correct Option: D

   Using Rule 1,
   3² + 4² = 5²
   ∴ Base = 3 cm and
   perpendicular = 4 cm
   ∴ Area of the right angled triangle
   

   =	1	× base × height
   	2

   
   

   =	1	× 3 × 4 = 6 sq.cm.
   	2

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854. The area of an equilateral triangle is 4√3cm². The length of each side of the triangle is :
     

1. 1. 3 cm
      

   
   
   

   2. 2√2 cm
      

   
   
   

   3. 2√3 cm
      

   
   
   

   4. 4 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 6,
   Area of the equilateral triangle
   

   =	√3	× side²
   	4

   
   

   ∴ 4√3 =	√3	× side²
   	4

   
   

   ⇒ side² =	4√3 × 4	= 16
   	√3

   
   ∴ Side = √16 = 4 cm

   Correct Option: D

   Using Rule 6,
   Area of the equilateral triangle
   

   =	√3	× side²
   	4

   
   

   ∴ 4√3 =	√3	× side²
   	4

   
   

   ⇒ side² =	4√3 × 4	= 16
   	√3

   
   ∴ Side = √16 = 4 cm

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855. The length of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. cm) of the triangle is
     

1. 1. 24
      

   
   
   

   2. 72
      

   
   
   

   3. 48
      

   
   
   

   4. 144

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 1,
   AG = 6 cm.
   
   

   BG =	2	× 12 = 8cm.
   	3

   
   

   GC =	2	× 15 = 10cm.
   	3

   
   

   Area of ∆ ABG =	1	× 6 × 8 = 24sq.cm.
   	2

   
   ∴ Area of ∆ ABC = 3 × 24 = 72 sq. cm.

   Correct Option: B

   Using Rule 1,
   AG = 6 cm.
   
   

   BG =	2	× 12 = 8cm.
   	3

   
   

   GC =	2	× 15 = 10cm.
   	3

   
   

   Area of ∆ ABG =	1	× 6 × 8 = 24sq.cm.
   	2

   
   ∴ Area of ∆ ABC = 3 × 24 = 72 sq. cm.

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