Question

If the altitude of an equilateral triangle is 5cm, then it's area equal to

Answer 1

Answer:

area of triangle=1/2*base*height

=1/2*5

=10

answer=10

Answer 2

The area of the triangle is 75✓3 cm².

Given data :

Height of the given equilateral triangle = 5 cm

• Before calculating the area of the triangle we have to also calculate the height of the triangle.

• Let,the length of one side of triangle = x cm ( assume x as a variable to calculate the length of one side of the triangle)

• Now, according to the mathematical formula we all know,

Height of an equilateral triangle = √3/2 × side of the triangle

• So, height of the given equilateral triangle = ✓3/2 × x = ✓3x/2 cm

• Now, let's compare our calculated height and the given height to form the below equation :

✓3x/2 = 5

x = (5×2)/✓3

x = 10/✓3

• So,the length of the one side of the triangle is 10/✓3 cm.

• Now,we have to calculate the area of the given equilateral triangle by using the following formula :

✓3/4 × (side)²

So,the area = ✓3/4 × (10✓3)² = ✓3/4 × 300 = 75✓3 cm²

Area of the given equilateral triangle is 75✓3 cm². (Answer)