Question

(1) Write the formula of half perimeter (s) in Heron's formula.​

Answer 1

Step-by-step explanation:

☆ Semi perimeter can be calculated as :-

Perimeter /2 i.e. half of perimeter.

Use in Heron's Formula :-

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

where s is the semi perimeter and a,b,c are the sides of traingle.

hope it will help you

Answer 2

Answer:

s = a+d+c/2.

Step-by-step explanation:

Heron's formula can also be written as

{\displaystyle A={\frac {1}{4}}{\sqrt {(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}}}A=\frac{1}{4}\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}

{\displaystyle A={\frac {1}{4}}{\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}}A=\frac{1}{4}\sqrt{2(a^2 b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)}

{\displaystyle A={\frac {1}{4}}{\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}}A=\frac{1}{4}\sqrt{(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)}

{\displaystyle A={\frac {1}{4}}{\sqrt {4(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{2}+b^{2}+c^{2})^{2}}}}{\displaystyle A={\frac {1}{4}}{\sqrt {4(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{2}+b^{2}+c^{2})^{2}}}}

{\displaystyle A={\frac {1}{4}}{\sqrt {4a^{2}b^{2}-(a^{2}+b^{2}-c^{2})^{2}}}.}A=\frac{1}{4}\sqrt{4a^2b^2-(a^2+b^2-c^2)^2}.