According to Heron's formula,the area of an e | vedclass

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

Question

(A) For an equilateral triangle with side length $a$,the semi-perimeter $s$ is given by $s = \frac{a+a+a}{2} = \frac{3a}{2}$.Heron's formula for the a

Vedclass · Accepted Answer

$(s-a) \sqrt{s(s-a)}$

Vedclass · Answer

(A) For an equilateral triangle with side length $a$,the semi-perimeter $s$ is given by $s = \frac{a+a+a}{2} = \frac{3a}{2}$.Heron's formula for the area of a triangle is $	ext{Area} = \sqrt{s(s-a)(s-b)(s-c)}$.Since $a = b = c$,the formula becomes $	ext{Area} = \sqrt{s(s-a)(s-a)(s-a)} = \sqrt{s(s-a)^3}$.This can be simplified as $	ext{Area} = \sqrt{s(s-a)^2 \cdot (s-a)} = (s-a) \sqrt{s(s-a)}$.

According to Heron's formula,the area of an equilateral triangle having each side $a$ is ..........

Similar Questions

From a point in the interior of an equilateral triangle,perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14 \, cm$,$10 \, cm$,and $6 \, cm$. Find the area of the triangle.

Area of a rhombus $=$ ............

Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

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

The measurements of the sides of a triangle are $12 \, cm$,$17 \, cm$,and $25 \, cm$. Find the area of this triangle. (in $, cm^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module