Question

Find the area of equilateral triangle of side 6cm by heron's formula by aglasem

Answer 1

Answer:

9$\sqrt{3}$ cm²

Step-by-step explanation:

heron's formula=$\sqrt{s(s-a)(s-b)(s-c)}$

s=semiperimeter=$\frac{a+b+c}{2} = \frac{6 + 6 + 6}{2} = \frac{18}{2} =9$

area=$\sqrt{9(9-6)(9-6)(9-6)} \\=\sqrt{9*3*3*3} \\=9\sqrt{3}$

So, the area is 9√3 cm².

For equilateral traingles, another formula derived from heron's formula is $\frac{\sqrt{3} a^{2} }{4}$

=$\frac{\sqrt{3}* 6^{2} }{4} \\= \frac{\sqrt{3} *36 }{4} \\= \sqrt{3} * 9\\=9\sqrt{3}$

Same answer but faster method ;-)

Answer 2

Answer:

81 cm^2

Step-by-step explanation:

side = 6

s=A+B+c/2

 = 6+6+6/2

= 9cm

therefore , area = √s(s-a)(s-b)(s-c)

                               = √9(9-6)(9-6)(9-6)

                                 = root {9 (3*3*3)}

                              =  root {9*3*3*3}

                              =27√9

                               = 81cm^2