Question

The height of an equilateral triangle is 15 cm. The area of the triangle is

• A. $$50\sqrt{3}sqcm$$
• B. $$70\sqrt{3}sqcm$$
• C. $$75\sqrt{3}sqcm$$
• D. $$150\sqrt{3}sqcm$$

Answer 1

Answer:

$$75\sqrt{3}sqcm$$

Let AB = BC = CA = 2a cm,

$AD = \sqrt{AB^2-BD^2}$

$=\sqrt{4a^2-a^2}$

=>\sqrt{3}a=15

$a=5\sqrt{3}$

$2a = Side = 10\sqrt{3} cm$

Area of triangle $=\frac{\sqrt{3}}{4}\times{(10\sqrt{3})^2}$

$= 75 \sqrt{3}$ sq. cm.