The height of an equilateral triangle is 9 mathrm~cm. Find its area (in mathrmcm2 ).

Question

The height of an equilateral triangle is 9 mathrm~cm. Find its area (in mathrmcm2 ). (A) 36 √3 (B) 27 √3 (C) 18 √3 (D) 9 √3

Tardigrade Admin · Accepted Answer

Let the side of the equilateral triangle be a mathrm~cm. text Given: (√3/2) a=9 ⇒ a=(18/√3) ⇒ a=6 √3 ∴ text Area =(√3/4) a2=(√3/4)(6 √3)2=27 √3 mathrm~cm2

Q. The height of an equilateral triangle is $9 cm$ . Find its area (in $cm^{2}$ ).

$363$

$273$

$183$

$93$

Let the side of the equilateral triangle be $a cm$ .
$Given: \frac{3}{2} a = 9 \Rightarrow a = \frac{18}{3} \Rightarrow a = 63$
$∴ Area = \frac{3}{4} a^{2} = \frac{3}{4} (63)^{2} = 273 cm^{2}$

Q. The height of an equilateral triangle is 9 cm. Find its area (in cm2 ).

363​

273​

183​

93​