Question

if each side of an equilateral triangle is halved , then find the ratio of an area of the area of new triangle to the area of the original triangle.

Answer 1

Answer:

$area \: of \: equilateral \: triangle \\ = \frac{ \sqrt{3} }{4} a ^{2} \\ area \: of \: new \: equi. \: triangle \\ = \frac{ \sqrt{3} }{4} { \frac{a}{2 ^{2} } }^{2} \\ ratio \: = (\frac{ \sqrt{3} }{4} \times \frac{ {a}^{2} }{4} ) \div ( \frac{ \sqrt{3 } a ^{2} }{4} ) \\ = \frac{1}{4}$