Question

Perimeter of equilateral triangle is equal to 180 cm. Find value of semi-perimeter (in cm)and area( square cm).

1)semiperimeter= 60,
area=300√3
2)semiperimeter= 90, area=900√3
3) semiperimeter= 120, area=1200√3
4) semiperimeter= 180, area=1500√3​

Answer 1

Given:-

• Perimeter of equilateral trianlge = 180cm

To find:-

• Semi - perimeter of the triangle
• Area of the triangle

Solution:-

We know,

Perimeter of an equilateral triangle = 3a

Therefore,

$\sf{3a = 180}$

$\sf{a = \dfrac{180}{3}}$

$\sf{a = 60cm}$

Now,

$\sf{Semi-perimeter = \dfrac{a+b+c}{2}}$

We know in an equilateral triangle all the sides are equal.

Therefore,

$\sf{s = \dfrac{60+60+60}{2}}$

= $\sf{s = \dfrac{180}{2}}$

= $\sf{s = 90}$

According to Heron's Formula

$\sf{Area = \sqrt{s(s-a)(s-b)(s-c)}}$

$\sf{Area = \sqrt{90(90-60)(90-60)(90-60)}}$

$\sf{Area = \sqrt{3\times3\times2\times5\times2\times3\times5\times2\times3\times5\times2\times3\times5}}$

$\sf{Area = 3\times2\times5\times3\times2\times5\sqrt{3}}$

$\sf{Area = 900\sqrt{3} {cm}^{2}}$ Option(2)

Another Formula for finding Area of an equilateral triangle:-

$\sf{\dfrac{\sqrt{3}{a}^{2}}{4}Sq.units}$

[Where a = side of the triangle]