Question



Perimeter = 36 cm

Heron’s formula: Area = 

What is the area of an equilateral triangle that has a perimeter of 36 centimeters? Round to the nearest square centimeter.

15 square centimeters

62 square centimeters

72 square centimeters

705 square centimeters

Answer 1

each side = 36/3 = 12 cm

semiperimeter = 36/2 = 18


`Area = √(18(18-12)(18-12)(18-12))= √(18 \cdot6\cdot6\cdot6)= √(3888) \approx 62`

Answer: 62 square centimeters

Answer 2

The answer is 62 square centimeters

Explanation:

Given perimeter is = 36 cm

So, each side will be =
`(36)/(3)=12` cm

Side according to formula is =
`(12+12+12)/(2)=18` cm

Now area is given as :

`A=√(s(s-a)(s-b)(s-c))` here a,b and c are sides.

=>
`A=√(18(18-12)(18-12)(18-12))`

=>
`A=√(18*6*6*6)`

=>
`A=√(3888)`

A= 62.35 ≈ 62 square cm

Therefore, the answer is option B : 62 square cm.