Question

(1) Find the area of an equilateral triangle whose
side is 10 cm.
10) Find the area of an equilateral triangle whose

height is 8 cm.​

Answer 1

1) ☆ Solution ☆

Given :-

• Side of an equilateral triangle is 10 cm.

To Find :-

• The area of an equilateral triangle.

Step-by-Step-Explaination :-

As we know that :-

Area of an equilateral triangle = √3/4 × side²

Putting the respective value,

Area of an equilateral triangle = √3 × (10)²/4

Area of an equilateral triangle = √3 × 100/4

Area of an equilateral triangle = 173.2/4

Area of an equilateral triangle = 43.3

Area of an equilateral triangle = 43.3 cm²

Hence,

Area of an equilateral triangle = 43.3 cm²

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10) ☆ Solution ☆

Given :-

• Height of an equilateral triangle is 8 cm.

To Find :-

• The area of an equilateral triangle.

Step-by-Step-Explaination :-

Let's the each side be x , half the base is x/2.

√{x²−(x/2)²}=8.

x²−x²/4=64.

3x²/4=64.

x²=64×4/3=2563.

x=√(256/3)=16(√3)/3.

Now,

Area = (√3)/4 side²

ares = (√3)/4 × [(16√3)/3]²

Area = (√3)/4 × 256×3/9

Area = 64/(√3)

Area = 36.95 cm²

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Answer 2

Question 1 :

Find the area of an equilateral triangle whose side is 10 cm.

Given :

Side of an equilateral triangle is 10 cm.

To find :

The area of an equilateral triangle.

Solution :

Area of an equilateral triangle = √3/4 × side²

Putting the value,

Area of an equilateral triangle = √3 × (10)²/4

Area of an equilateral triangle = √3 × 100/4

Area of an equilateral triangle = 173.2/4

Area of an equilateral triangle = 43.3

Area of an equilateral triangle = 43.3 cm²

Final Solution :

Hence,

Area of an equilateral triangle = 43.3 cm².

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Question 10 :

Find the area of an equilateral triangle whose height is 8 cm.

Given :

Height of an equilateral triangle is 8 cm.

To find :

The area of an equilateral triangle.

Solution :

Let the each side be x , half the base is x/2.

√{x² − (x/2)²} = 8.

x²−x²/4 = 64.

3x²/4 = 64.

x² = 64 × 4/3 = 2563.

x = √(256/3) = 16(√3)/3.

Now,

Area = (√3)/4 side²

ares = (√3)/4 × [(16√3)/3]²

Area = (√3)/4 × 256×3/9

Area = 64/(√3)

Area = 36.95 cm²

Final solution :

Hence,

Area of an equilateral triangle = 36.95 cm².

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Additional Information :

Know More :

Perimeter of Rectangle = 2 ( l + b )

Perimeter of Square = 4 × side

Perimeter of Triangle = 3 × side

Area of Rectangle = L × B

Area of Square = ( side ) ²

Area of Rhombus = Product of Diagonal/2.

Area of Parallelogram = Base × Height.

Area of triangle = 1/2 × base × height

Thank you.