Question

if the perimeter of an equilateral triangle is 180 m. then its area in cm2 will be a. 9000000cm2 b. 9000000√3cm2 c. 3000000√3cm2 d. 60000√3 cm2

Answer 1

Answer:

The area of the given equilateral triangle is $9000000\sqrt{3}cm^{2}$. That is, either option (a) or option (b).

Step-by-step explanation:

Perimeter of the equilateral triangle is given as 180m.

Hence the length of a side of the equilateral triangle = 180m ÷ 3 = 60m.

We have to calculate the area of the triangle in cm², but the perimeter and hence side calculated is in meters. Hence we have to convert this into cm before calculating the area.

1m = 100cm

∴ 60m = 60 × 100cm

           = 6000cm.

Now let us calculate the area of the given equilateral triangle. The formula for calculating the area of an equilateral triangle is

Area = $\frac{\sqrt{3} }{4} a^{2}$

where a is the length of one side.

Here a = 6000cm

∴ Area = $\frac{\sqrt{3} }{4} \times 6000^{2}$

           =  $9000000 \sqrt{3} cm^{2}$.

Therefore the area of the given equilateral triangle is $9000000\sqrt{3}cm^{2}$