Question

ABC is an equilateral triangle with perimeter 30 cm p q and R are midpoints of A B and C respectively find the area of triangle pqr

Answer 1

Answer: The area of triangle pqr would be 10.83 cm^2.

Step-by-step explanation:

Given that,

Perimeter of equilateral triangle ABC= 30 cm

We know all the three sides of equilateral triangle are equal. So,

Each side of equilateral triangle= perimeter/3= 30/3= 10 cm

Area of equilateral triangle= (sqrt3)/4*a^2 where a is side of equilateral triangle.

So,

Area of equilateral triangle ABC= (sqrt3)/4*10^2=(sqrt3)/4*100=25*sqrt3

Area(ABC)= 43.30 cm^2

We know from the symmetry, triangle made by the midpoints of equilateral triangle divides the equilateral triangle into 4 equal parts.

So,

Area(pqr)=1/4*area(ABC)= 1/4*43.30

Area(pqr)=10.83 cm^2