Question

6. Calculate the area of an equilateral triangle of side 12 cm,
correct to two decimal places. Also, find its height correct to one
decimal place. (Take V3 = 1.732).

Answer 1

→ Given ←

Side of an equilateral triangle, a = 12 cm

$\rule{180}2$

→ To Find ←

• The area of the equilateral triangle
• The height of the triangle(h).

$\rule{180}2$

→ We Must Know ←

Area of an equilateral triangle :-

$\sf{A=\dfrac{\sqrt{3} }{4}a^2 }$

Area of a triangle :-

$\sf{A=\dfrac{1}{2} \times Base \times Height }$

Where, base = a (in an equilateral triangle)

$\rule{180}2$

→ Solution ←

Area of the triangle :-

$\sf{A=\dfrac{\sqrt{3} }{4}(12)^2 }\\\\\sf{\dashrightarrow A=\dfrac{1.732}{4} \times 12 \times 12 }\\\\\sf{\dashrightarrow A=1.732 \times 12 \times 3 }\\\\\sf{\dashrightarrow A=1.732 \times 36}\\\\ \sf{\dashrightarrow A=62.352\ cm^2}\\\\\large\boxed{\boxed{\sf{\color{lime}{\dashrightarrow A=62.35\ cm^2}}}}$

______________

Now, putting the values for the height of the triangle :-

$\sf{A=\dfrac{1}{2} \times Base \times Height }\\\\\sf{\dashrightarrow 62.35 = \dfrac{1}{2}\times 12 \times h }\\\\\sf{\dashrightarrow 62.35=6h}\\\\\sf{\dashrightarrow h=\dfrac{62.35}{6} }\\\\\sf{\dashrightarrow h=10.39\ cm }\\\\\large\boxed{\boxed{\sf{\color{lime}{\dashrightarrow h=10.4\ cm}}}}$

Answer 2

Given :

• The area of an equilateral triangle of side 12 cm.

To find :

• Area of the equilateral triangle =?

• Height of the equilateral triangle =?

Step-by-step explanation :

Side of the equilateral triangle = 12 cm.

As We know that,

Area of equilateral traingle = ( √3 / 4 ) a²

Substituting the values in the above formula, we get,

= (1.732/4) × 12² (√3 = 1.732).

= 1.732 × 3 × 12

= 5.196 × 12

= 62.352

Correct to two decimal places.

Therefore, Area of the equilateral triangle = 62.35 cm².

Now height of the equilateral triangle,

We know that,

Side (a) = (2h)√3

Substituting the values in the above formula, we get,

12 = 2h × 1.732

h = 6 × 1.732

h = 10.39

Correct to one decimal places.

Therefore, Height of the equilateral triangle = 10.3 cm