Question

Area of an equilateral triangle with side length a is equal to: *

1 point

(a)√3/2a

(b)√3/2a2

(c)√3/4 a2

(d)√3/4 a

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Answer 1

Step-by-step explanation:

option c is correct one

Answer 2

Given - Type of triangle = equilateral triangle

Side length of triangle = a

Find - Area of triangle

Solution - For an equilateral triangle, let the sides be AB and AC. The base be AB and altitude be AD.

Now, AB is a, BD is a/2. We will find AD.

As this will form of right angles triangle, keeping the values in Pythagoras theorem to calculate AD.

AB² = AD² + BD²

AD² = a² - (a/2)²

AD² = a² - a²/4

AD² = (4a² - a²)/4

AD² = 3a²/4

AD = ✓(3a²/4)

AD = ✓3a/2

Now calculating area of triangle by the formula = 1/2 * base * height.

Base BC is a and height AD is ✓3a/2

Keeping the values in formula-

Area of triangle = 1/2*a*✓3a/2

Area of triangle = (a²✓3)/4

Thus, area of triangle is (c)√3/4 a2.