Question

What is the area of an isosceles triangle with base $4$ cm and the length of one of the equal sides is $8$cm?

Answer 1

S= semiperimeter

$S=\frac{a+b+c}{2}$

$=\frac{4+8+8}{2}=10$

By Heron's Formula,

$A\left(\Delta ABC\right)=\sqrt{S(S-a)(S-b)(S-c)}$

$=\sqrt{10(10-4)(10-8)(10-8)}$

$=\sqrt{10\times 6\times 2\times 2}$

$=2\sqrt{60}$

$=2\times \sqrt{4\times 15}=2\times 2\sqrt{15}$

$=4\sqrt{15}c{m}^2$