The area of an equilateral triangle is equal | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The area of an equilateral triangle with side length $a$ is given by the formula: Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$. Fo

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{4}(	ext{side})^2$

Vedclass · Answer

(D) The area of an equilateral triangle with side length $a$ is given by the formula: Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$. For an equilateral triangle,the base is $a$ and the height $h$ is calculated using the Pythagorean theorem: $h = \sqrt{a^2 - (a/2)^2} = \sqrt{3a^2/4} = \frac{\sqrt{3}}{2}a$. Substituting these values: Area $= \frac{1}{2} 	imes a 	imes \frac{\sqrt{3}}{2}a = \frac{\sqrt{3}}{4}a^2$. Therefore,the correct option is $D$.

The area of an equilateral triangle is equal to ............

Similar Questions

If the area of an equilateral triangle is $16 \sqrt{3} \, cm^{2}$,then the perimeter of the triangle is (in $cm$)

The base of a right triangle is $8 \, cm$ and its hypotenuse is $10 \, cm$. Its area will be (in $cm^2$):

$A$ triangle and a parallelogram have the same area. If the sides of the triangle are $10 \, cm$,$17 \, cm$,and $21 \, cm$,and the parallelogram stands on the base $12 \, cm$,find the height of the parallelogram. (in $, cm$)

The area of a trapezium is $475 \, cm^2$ and the height is $19 \, cm$. Find the lengths of its two parallel sides if one side is $4 \, cm$ greater than the other.

The perimeter of a triangular field is $420\, m$ and its sides are in the ratio $6: 7: 8$. Find the area of the triangular field (in $m^2$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module