Question

Find the area of an isosceles triangle whose base is 6cm and perimeter is 16cm using heron formula

Answer 1

Answer:12sq.cm

Step-by-step explanation:(16-6)/2=5cm

Hence sides are 5cm 5cm 6cm it’s area will give 12sq.cm

Answer 2

Perimeter = 16cm

Base = 6cm

Let the unknown sides be x.

(Two sides of an isosceles triangle are equal)

Perimeter = 16cm

$x + x + 6 = 16 \\ 2x + 6 = 16 \\ 2x = 16 - 6 \\ 2x = 10 \\ x = \frac{10}{2} \\ x = 5$

$a = 5 \: \\ b = 5 \: \\ c = 6 \\ s = \frac{a + b + c}{2} \\ = \frac{5 + 5 + 6}{2} \\ = \frac{16}{2} = 8$

$using \: herons \: formula \\ \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{8(8 - 5)(8 - 5)(8 - 6)} \\ = \sqrt{8 \times 3 \times 3 \times 2} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3} \\ = 2 \times 2 \times 3 = {12cm}^{2}$