Question

The hcight of an equilateral triangle is 15 cm. The
area of the triangle is-
a) 50/3 sq. cm. b) 70/3 sq. cm.
c) 753 sq. cm. d) 150/3 sq. cm​

Answer 1

Answer:

$Area (A) = 75\sqrt{3}\: cm^{2}$

Step-by-step explanation:

$Given\: Height \: of \: an \\equilateral \: triangle (h)=15\:cm$

$Side = a \:cm$

$we\: know \: that \\ \frac{\sqrt{3}}{2}a=h$

$\implies \frac{\sqrt{3}}{2}a=15$

$\implies a = \frac{15\times 2}{\sqrt{3}}\\=\frac{30}{\sqrt{3}}\:--(1)$

$Now,\\Area(A) = \frac{\sqrt{3}}{4} a^{2}$

$= \frac{\sqrt{3}}{4} \left(\frac{30}{\sqrt{3}}\right)^{2}$

$= \frac{\sqrt{3}}{4}\times \frac{900}{3}$

$=75\sqrt{3}\: cm^{2}$

Therefore,

$Area (A) = 75\sqrt{3}\: cm^{2}$

Given options are wrong .

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