# If the Length of a Median of an Equilateral Triangle is X Cm, Then Its Area is - Mathematics

MCQ

If the length of a median of an equilateral triangle is x cm, then its area is

#### Options

• x2

• $\frac{\sqrt{3}}{2} x^2$

• $\frac{x^2}{\sqrt{3}}$

• $\frac{x^2}{2}$

#### Solution

We are given the length of median of an equilateral triangle by which we can calculate its side. We are asked to find area of triangle in terms of x

Altitude of an equilateral triangle say L, having equal sides of cm is given by, where, L = x cm

x = sqrt(3)/2 a

a = 2/sqrt(3) x  cm

Area of an equilateral triangle, say A1 having each side a cm is given by

A_1 = sqrt(3)/4 a^2

Since a = 2/sqrt(3) x  cm .So

A_1 = sqrt (3)/4 (2/sqrt(3) x )^2

A_1 = sqrt(3)/4 xx (4x^2)/3

A_1 = x^2/sqrt(3)

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.4 | Q 13 | Page 25

Share