Question

find the area of tringle. whose sides are 8cm and 11cm and perimeter of tringle is 32cm

Answer 1

Let the 3rd side is x

P of triangle = 8 + 11 + x

19 + x = 32

x = 32-19 = 13cm

Now use heron formula for finding area.

$s = (a + b + c) \div 2$

$s= (11 + 8 + 13) \div 2$

$s = 32 \div 2 = 16$

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

$\sqrt{16(16 - 11)(16 - 8)(16 - 13)}$

$\sqrt{16 \times 5 \times 8 \times 3}$

$\sqrt{4 \times 4 \times 5 \times 2 \times 2 \times 2 \times 3}$

$4 \times 2 \sqrt{5 \times 2 \times 3}$

$8 \sqrt{30} cm {}^{2}$